B.Sc Corporate Statistics Question Paper 2008

Loyola College B.Sc. Statistics April 2008 Statistical Process Control Question Paper PDF Download

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

NO 30

 

SIXTH SEMESTER – APRIL 2008

ST 6602 – STATISTICAL PROCESS CONTROL

 

 

 

Date : 23/04/2008                Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

 

 

PART – A

Answer ALL the questions:                                                                          (10 x 2 = 20)

 

  1. Mention the reasons for Quality improvement in a new business strategy.
  2. What is TQM philosophy?
  3. What is the Box plot?
  4. Explain the Stem and Leaf plot.
  5. Define Statistical Process control.
  6. What benefits are expected out of the use of control charts?
  7. What is a CUSUM chart?
  8. Define process capability analysis and mention its purpose.
  9. Mention disadvantages of Acceptance sampling.
  10. What is item – by – item sequential sampling plan?

 

 

PART – B

Answer any FIVE  questions.                                                                      (5 x 8 = 40)

 

  1. Explain how variation is described through the frequency distribution and histogram.
  2. Explain the link between Quality improvement and productivity.
  3. How will you prepare the control charts for fraction defectives?
  4. Distinguish between CUSUM chart and Shewhart chart.
  5. Discuss the process capability analysis using a control chart.
  6. How can the Shewhart control charts be interpreted to draw meaningful conclusions?
  7. What is acceptance sampling? Mention the situations it is most likely to be useful.
  8. Describe the operating procedure of double sampling plan.

 

PART – C

Answer any TWO   questions.                                                                      (2 x 20 = 40)

  1. a) State the specific functional responsibilities of total Quality Management.
  1. b) A TV voltage stabilizer manufacturer checks the quality of 50 units of his product nonconforming units are as follows.

 

Days: 1 2 3 4 5 6 7 8 9
Fraction defectives: 0.10 0.20 0.06 0.04 0.16 0.02 0.08 0.06 0.02

 

Days: 10 11 12 13 14 15
Fraction defectives: 0.16 0.12 0.14 0.08 0.10 0.06

Construct 3 – sigma trial Control limits for fraction defectives and comment on it.

(12+8)

 

 

 

 

  1. a) How do you set the Control limits for R-charts in Statistical quality control?
  1. b) Sixteen boxes of electric switches each containing 20 switches were randomly selected from a lot of switch boxes and inspected for the number of defects per box. The numbers of defects per box were as follows:

 

Box Numebr: 1 2 3 4 5 6 7 8 9 10
No. of defects: 12 15 9 14 18 26 8 6 11 12

 

Box Number: 11 12 13 14 15 16
No. of defects: 16 13 19 18 14 21

 

Calculate 3-sigma limits for c-chart and draw conclusion.                             (12+8)

 

  1. a) Describe the operational aspects of CUSUM charts and the role of v-mask.
  1. b) How can sequential sampling plan be implemented graphically under SPRT? (12+8)
  1. a) Explain the Operating procedure of Single Sampling plan and obtain its OC curve.
  1. b) What are continuous sampling plans and mention a few situations where these plans are applied. (12+8)

 

 

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Loyola College B.Sc. Statistics April 2008 Statistical Methods Question Paper PDF Download

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

NO 1

 

FIRST SEMESTER – APRIL 2008

ST 1500 – STATISTICAL METHODS

 

 

 

Date : 03/05/2008                Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

PART – A

                                                                                    (10 x 2 = 20 marks)

Answer ALL the questions.

 

  1. Distinguish between Census and sample.
  2. State the objectives of classification of data.
  3. Why do we call Arithmetic mean is a good average?
  4. When do you say a distribution is skewed? Sketch positive and negative skew ness.
  5. What is curve fitting?
  6. Write down the normal equations for fitting .
  7. If for two variable X and Y, correlation coefficient

find the regression co efficient of X onY.

  1. If two regression lines are  and  for two variables X and Y, find the mean values of X and Y.
  2. In a report on consumers preference, it was given that out of 500 persons surveyed 410 preferred variety A, 380 preferred variety B and 270 persons liked both. Are the data consistent?
  3. State any two characteristics of Yule’s coefficient of Association.

 

PART – B

                                                                                                (5 x 8 = 40 marks)                 

Answer any 5 questions.      

 

  1. Draw  ogive curves for the data given below:
Draw Sales

(Rs.000)

 10-20 20-30 30-40 40-50 50-60 60-70 70-80
No. of Shops 3 6 10 15 8 4 2

 

  1. Distinguish between Classification and Tabulation.

 

  1. Calculate Karl Pearson’s Co efficient of Skewness for the data given below. On the basis of mean, median and standard deviation.
Wages: 5 6 7 8 9 10 11 12
Workers: 25 45 65 100 30 75 40 50

 

  1. Bring out the relationship between to the following data:
x: 0 1 2 3 4
y: 1 1.8 1.3 2.5 2.3

 

  1. Fit a parabola of second degree to the following data
x: 0 1 2 3 4
y: 1 1.8 1.3 2.5 2.3

 

  1. What do you understand by regression? Why there are two regression equations? What are its uses?
  2. From the following data, calculate the coefficient of rank correlation between X and Y
X: 36 56 20 65 42 33 44 50 15 60
Y: 50 35 70 25 58 75 60 45 80 38

 

  1. 1660 candidates appeared for a competitive examination. 422 were successful, 256 had attended a coaching class, and of these 150 came out successful. Estimate the utility of the coaching classes.

 

PART – C

                                                (2 x 20 = 40 marks)

Answer any TWO questions.

 

  1. a) Calculate mean deviation from median from the following data.
Class Interval: 20-25 25-30 30-40 40-45 45-50 50-55
Frequency: 6 12 17 30 10 10

 

Class Interval: 55-60 60-70 70-80
Frequency: 8 5 2

 

  1. b) From the prices of shares X and Y given below, state which share is more stable in value

 

  1.  It is known that the readings for x and y given below should follow a law of the form , where a and b are constants
x: 1 2 3 4 5 6 7 8
y: 5.43 6.28 8.23 10.32 12.63 14.86 17.27 19.51

use the method of least squares to find the best values of a and b.

 

  1. Calculate and from the data given below
Marks: 0-10 10-20 20-30 30-40 40-50 50-60 60-70
No. of Students: 8 12 20 30 15 10 5

 

  1. Calculate the two regression equations Y on X and X on Y and correlation coefficient     .
Price (Rs): 10 12 13 12 16 15
Amount

Demanded

 40 38 43 45 37 43

Also estimate the likely demand when the price is Rs.20.

 

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Loyola College B.Sc. Statistics April 2008 Statistical Mathematics – II Question Paper PDF Download

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

NO 12

 

THIRD SEMESTER – APRIL 2008

ST 3501 / 3500 – STATISTICAL MATHEMATICS – II

 

 

 

Date : 26/04/2008                Dept. No.                                        Max. : 100 Marks

Time : 1:00 – 4:00

 

SECTION – A

Answer ALL the Questions                                                                    (10 x 2 = 20 marks)

 

  1. Define Upper and Lower Sums of a function corresponding to a given partition of a closed interval.
  2. State the Second Mean Value theorem for integrals.
  3. If f(x) = C x2 (1 – x), for 0 < x < 1 is a probability density function (p.d.f.), find the value of C.
  4. Define improper integral of second kind.
  5. Show that the improper integral  converges (where a > 0)
  6. Find L–1
  7. State the general solution for the linear differential equation  + Py = Q
  8. State the postulates of a Poisson Process.

 

  1. State the Fundamental Theorem on a necessary and sufficient condition for the consistency of a system of equations  A+ = .
  2. If λ is a characteristic root of A, show that λ2 is a characteristic root of A2.

 

SECTION – B

Answer any FIVE Questions                                                                  (5 x 8 = 40 marks)

 

  1. Let Pn = {0, 1/n, 2/n, ….., (n – 1)/n, 1} be a partition of [0, 1]. For the function f(x) = x, 0 ≤x ≤ 1, find U[Pn, f] and L[Pn, f]. Comment on the integrability of the function.
  2. Evaluate: (i)  (ii)
  3. Show that the integral (where a > 0) converges for p > 1 and diverges for p ≤ 1.

 

  1. Define Beta integrals of First kind and Second kind. Show that one can be obtained from the other by a suitable transformation.

(P.T.O)

  1. Solve:  =

 

  1. Solve: (D2 + 4D + 6) y = 5 e– 2 x

 

  1. Establish the relationship between the characteristic roots and the trace and determinant of a matrix.

 

  1. Give a parametric form of solution to the following system of equations:

4x1 – x2 + 6x3 = 0

2x1 + 7x2 +12x3 = 0

x1 – 4x2 – 3x3 = 0

5x1 – 5x2 +3x3 = 0

 

SECTION – C

 

Answer any TWO Questions                                                                 (2 x 20 = 40 marks)

 

  1. (a) State and prove the First Fundamental Theorem of Integral Calculus.

(b) Evaluate (i)  (ii)                                                      (12+8)

 

  1. (a) Show that mean does not exist for the distribution with p.d.f.

f(x) = , – ∞ < x < ∞

(b)L[f(t)] = F(s), show that L[t f(t)] = – F(s). Using this result find L[t2 e– 3 t]

(8+12)

 

  1. Evaluate: (a) ∫ ∫ x2 y2 dx dy over the circle x2 + y2 ≤ 1.

(b) ∫ ∫ y dx dy over the region between the parabola y = x2 and the line x + y = 2

(10+10)

 

  1. (a) State and Prove Cayley-Hamilton Theorem.

(b) If P is a non-singular matrix and A is any square matrix, show that A and      P–1AP have the same characteristic equation. Also, show that if ‘x’ is a characteristic vector of A, then P–1 x is a characteristic vector of P–1AP.      (12+8)

 

 

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Loyola College B.Sc. Statistics April 2008 Statistical Mathematics – I Question Paper PDF Download

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034           LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034B.Sc. DEGREE EXAMINATION – STATISTICSSECOND SEMESTER – APRIL 2008ST 2500 – STATISTICAL MATHEMATICS – I
Date : 23/04/2008 Dept. No.         Max. : 100 Marks                 Time : 1:00 – 4:00                                               SECTION – A

Answer ALL the Questions                                                                    (10 x 2 = 20 marks)
1. Define an r-permutation of n objects.2. Define mutually exclusive events.3. An urn contains 6 white, 4 red and 9 black balls. If 2 balls are drawn at random find the probability that both are red. 4. Define probability mass function (p.m.f.) of a random variable.5. State any two properties of a distribution function.6. Write down the p.m.f. of a Poisson distribution.7. Define an oscillating sequence and give an example.8. Define a monotonic sequence with an example.9. Define ‘Sequence of Partial Sums’ for a series.10. State Cauchy’s Root test.
SECTION – BAnswer any FIVE Questions                                                                    (5 x 8 = 40 marks)
11. State the ‘Addition Theorem of Probability’. Applying the theorem, find the probability that a number chosen at random from 1 to 40 is a multiple of 2 or 5.12. Two digits are chosen one by one at random without replacement from  {1, 2, 3, 4, 5}. Find the probability that (i) an odd digit is selected in the first draw; (ii) an odd digit is selected in the second draw, (iii) odd digits are selected in both draws.13. Show that the sequence an =   converges and that its limit lies between 2 and 3.14. If  sn = L and  tn = M, show that  (sn+ tn) = L + M and s¬n.tn =    L. M15. Two fair dice are rolled. Let X = Sum of the two numbers that show up. Obtain the distribution function of X.16. State the D’Alembert’s Ratio Test. Applying it, test for convergence of the series  .17. State the ‘Limit form of Comparison test’. Applying it, test whether the series   +    +   +    + ………. converges or diverges.18. Define a Binomial distribution. If 10 fair coins are thrown, find the probability of getting (i) Exactly 5 heads, (ii) At least 7 heads.

 

(P.T.O)

SECTION – CAnswer any TWO Questions                                                                 (2 x 20 = 40 marks)
19. (a) State and Prove Baye’s Theorem.            (b) A factory produces a certain type of outputs by three machines. The daily                production figures by the three machines are 3000 units, 2500 units and 4500               units. The percentages of defectives produced by the three machines are 1 %, 1.2               % and 2 %. An item is drawn at random from a day’s production and is found to               be defective. What is the probability that the defective came from (i) machine 1,               (ii) Machine 2, (iii) Machine 3?                                                                 (10 +10)
20. (a) Show that the sequence sn =   +   + ……. +   is convergent.              State the result that you use here.(b) A random variable X has the following probability distribution:         x  :    –3      6         9      p(x):     1/6    1/2     1/3       Find E(X), Var(X) and E(2 X+1)                                                           (10 +10) 21. Discuss the convergence of the following series: (a)   (b)                                                                                                                       (10 +10)
22. (a) Give the logarithmic series and show that it is convergent for |x | < 1.       (b)  Discuss the convergence of the geometric series  .                      (10+10)

 

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Loyola College B.Sc. Statistics April 2008 Statistical Mathematics – I Question Paper PDF Download

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

NO 5

 

SECOND SEMESTER – APRIL 2008

ST 2501 – STATISTICAL MATHEMATICS – I

 

 

 

Date : 23/04/2008                Dept. No.                                        Max. : 100 Marks

Time : 1:00 – 4:00

 

SECTION – A

Answer ALL the Questions                                                                    (10 x 2 = 20 marks)

 

  1. Define a bounded function and give an example.
  2. Write the formula for an for the sequence 1, –3, 5, –7, . . . .
  3. State any two properties of a distribution function.
  4. Give reason (state the relevant result) as to why the series  is divergent.
  5. State the Limit Form of Comparison Test.
  6. For the function f(x) = | x |, x  R, find f ‘(0 +) and f ‘(0 –).
  7. Define ‘Stationary Point’ of a function.
  8. Is the space V   = { (x1, x2, 2x1 – x2) | x1, x2  R }a vector subspace of R3 ? Justify your answer.
  9. Define symmetric matrix
  10. Define rank of a matrix.

 

SECTION – B

Answer any FIVE Questions                                                                    (5 x 8 = 40 marks)

 

  1. Show that the function f(x) = xn is continuous at every point of R
  2. Show that a convergent sequence is bounded. Give an example to show that the converse is not true.
  3. Show that the series 1 + + + + · · · · · ·    is convergent
  4. Find the m.g.f. of the random variable with p.m.f. p(x) = p qx, x = 0, 1, 2, ….

Hence find the mean.

  1. Verify the Mean Value theorem for the function f(x) = x2 +3x – 4   on the interval [1, 3].
  2. Examine the continuity of the following function at the origin (by using first principles):

f(x) =

  1. Verify whether the vectors [2, –1, 1]’, [1, 2, –1]’, [1, 1,–2]’ are linearly independent or dependent.
  2. Find the rank of the matrix

(P.T.O)

 

 

 

SECTION – C

Answer any TWO Questions                                                                 (2x 20 = 40 marks)

 

  1. (a) If f(x) = ℓ1 and g (x) = ℓ2 ≠ 0, then show that  = ℓ1 / ℓ2

(b) If p(x) = x / 15,  x = 1, 2, 3, 4, 5 be the probability mass function of a random variable X, obtain the distribution function of X.                                          (12+8)

 

  1. (a) State the Cauchy’s condensation Test and using it discuss the convergence of the series for variations in ‘p’.

(b) Check whether the following series are conditionally convergent / absolutely convergent / divergent:

(i)   (ii)                                           (10+10)

 

  1. (a) Obtain the Maclaurin’s Series expansion for the function f(x) = log (1 + x). Show that the expansion indeed converges to the function for –1 < x < 1 by analyzing the behaviour of the remainder term(s).

(b) Discuss the extreme values of the function f(x) = 2 x3 – 15 x2 + 36 x + 1

(14+6)

 

  1. (a) Establish the uniqueness of the inverse of a non-singular matrix. Also, establish the ‘Reversal Law’ for the inverse of product of two matrices.

(b) Find the inverse of the following matrix by using any method:

(8+12)

 

 

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Loyola College B.Sc. Statistics April 2008 Resource Management Techniques Question Paper PDF Download

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

NO 6

 

B.Sc. DEGREE EXAMINATION – STATISTICS

THIRD SEMESTER – APRIL 2008

ST 3103 / 3100 – RESOURCE MANAGEMENT TECHNIQUES

 

 

 

Date : 07/05/2008                Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

SECTION- A

Answer all the questions.                         10×2 =  20 marks

1.Define operations research.

2.Explain the need for slack and surplus variables in an LPP.

3.Define basic solution for an LPP.

4.State the objective of  a  transportation  problem.

5.Express an assignment problem as an LPP.

6.Distinquish between CPM and PERT.

7.When is an activity in a network analysis called critical ?

8.Define degenerate solution  for a transportation problem.

9.What  is time horizon and lead time in inventory ?

10 Write a short   note on setup  and  shortage costs.

SECTION –B

Answer any five questions.                         5×8 = 40 marks

11.Obtain all the basic solutions to the following system of linear equations:

2x1 + x2 – x3 = 2

3x1 + 2x2 + x3 = 3.

12.Solve graphically the following LPP:

Max Z = 7x1 + 3x2

Subject to the constraints:

x1 + 2x2    3

x1 + x2     4

x1  5/2

x2  3/2

x10 & x2  0.

13.Find an initial solution for the following transportation problem using least cost

method:

Destination

Origin                    ————————————       Availability

D1        D2     D3      D4

——————————————————————————

O1                           1            2        1         4                        30

O2                           3            3        2         1                        50

O3                           4            2        5         9                        20

Requirement         20          40      30       10

——————————————————————————-

14.Six wagons are available at six stations A,B,C,D,E and F. These are required at

stations I,II,III,IV,V and VI. The following table gives the distances(in kilometers)

between various stations:

I           II         III        IV        V         VI

A     20         23        18        10        16        20

B     50         20        17        16        15        11

C     60         30        40        55        8          7

D      6          7          10        20        100      9

E      18         19        28        17        60        70

F       9          10        20        30        40        55

How should the wagons be assigned so that the total distance covered is minimized ?

  1. A small maintenance project consists of the following 12 jobs:

Job                         Duration(in days)

  • 2

2-3                              7

2-4                               3

3-4                               3

3-5                               5

4-6                               3

5-8                               5

6-7                               8

6-10                             4

7-9                               4

8-9                               1

9-10                             1

(a) Draw the arrow diagram of the project.

(b) Determine the critical path and the project duration.

  1. Use simplex method to solve the following LPP:

Max Z = 3x1 + 2x2

Subject to the constraints:

x1+ x2   4

x1 – x2   2

x10, x20

  1. Explain the inventory control of a system.
  2. Derive a single item static model with the necessary diagram.

SECTION-C

Answer any two questions.                    2×20 = 40 marks

  1. Use big M method to

Min Z = 4x1+ 3x2

Subject to the constraints:

2x1 + x2  10

-3x1 +2x2 6

x1 + x2  6

x10,x20

  1. Consider the following transportation table showing production and transportation

costs , along with the supply and demand positions of factories/distribution centres:

M1                 M2                   M3                   M4                   Supply

——————————————————————————-

F1                          4                    6                      8                       13                   500

F2                        13                    11                    10                    8                     700

F3                        14                    4                      10                    13                   300

F4                         9                     11                    13                    3                     500

——————————————————————————–

Demand               250                 350                  1050                200

(a) Obtain an initial basic feasible solution by using VAM.

(b) Find the optimal solution for the above given problem.

  1. A project is composed of eleven activities ,the time estimates for which are given below:

——————————————————————————————————-

Activity                 optimistic time              normal time                        pessimistic time

(days)                           (days)                                    (days)

——————————————————————————————————–

1-2                                  7                                     9                                              17

1-3                                  10                                   20                                            60

1-4                                  5                                     10                                            15

2-5                                  50                                   65                                            110

2-6                                  30                                   40                                            50

3-6                                  50                                   55                                            90

3-7                                   1                                    5                                              9

4-7                                  40                                   48                                            68

5-8                                  5                                     10                                            15

6-8                                  20                                   27                                            52

7-8                                  30                                   40                                            50

(a) Draw the network diagram for the project.

(b) Find mean and variance of the activities.

(c) Determine the critical path.

(d) What is the probability of completing the project in 125 days ?

22.(a) Derive the single item static model with one price break with the necessary diagrams.

(b) LubeCar specializes in fast automobile oil change.The garage buys car oil in bulk

at $3 per gallon.A price discount of $2.50  per gallon is available if LubeCar

purchases more than 1000 gallons.The garage services approximately 150 cars per

day,and each oil change requires 1.25 gallons. LubeCar stores bulk oil at the cost

of $0.02 per gallon per day.Also the cost of placing an order for bulk oil is

$20.There is a 2 day lead time for delivery.Determine the optimal inventory policy.

 

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Loyola College B.Sc. Statistics April 2008 Probability And Random Variables Question Paper PDF Download

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

NO 2

           B.Sc. DEGREE EXAMINATION – STATISTICS

FIRST SEMESTER – APRIL 2008

ST 1501 (PROBABILITY AND RANDOM VARIABLES)

 

 

 

Date : 06-05-08                  Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

 

SECTION –A

 

Answer ALL the questions.                                                                         (10×2=20 marks)

 

  1. State the mathematical definition of probability.
  2. A, B and C are three mutually exclusive and exhaustive events associated with a random experiment. Find given .
  3. If A, B and C are three arbitrary events, find expressions for the events given below:
  1. Both A and B but not C occur
  2. At least one occur
  1.  Two dice are tossed. Find the probability of getting an even number on the first die.
  2. For any event , show that A and null even are independent.
  3. The odds in favour of manager X settling the wage dispute with the workers are 6:8 while the odds in favour of manager Y settling the same dispute are 14:16. What is the probability that the dispute is settled?
  4. Define ‘aprior’ and ‘posterior’ probabilities.
  5. A university has to select an examiner from a list of 50 persons – 20 of them being women and 30 men, 10 of them know Tamil and 40 not, 15 of them are teachers while the remaining 35 are not. What is the probability that the University selects a Tamil knowing woman teacher?
  6. Define a random variable.
  7. If X is a random variable and ‘a’, ‘b’ are constants, then show that .

 

SECTION –B

Answer any FIVE questions.                                                           (5×8=40 marks)

 

  1.  If , then show that

 

  1. Twenty five books are placed at random in a shelf. Find the probability that a particular pair of books shall be (i) always together and (ii) never together.
  2. If A1, A2, …, An are ‘n’ events, then show that
  3. Three newspapers A, B and C are published in a certain city. It is estimated from a survey that, out of the adult population 20% read A, 16% read B, 14% read C, 8% read both A and B, 5% read both A and C, 4% read both B and C, 2% read all the three. Find what percentage read atleast one of the papers.
  4. An urn contains four tickets marked with numbers 112, 121, 211, 222 and one ticket is drawn at random. Let Ai , i=1,2,3 be the event that the ith digit of the number of the ticket drawn is 1. Discuss the independence of the events A1, A2 and A3.

 

 

  1. A random variable x has the following probability mass function:
x: 0 1 2 3 4 5 6 7
p(x): 0 k 2k 2k 3k k2 2k2 7k2+k
  1. i) Find k ii) Evaluate
  1. Let X be a random variable with the following probability distribution:
x: -3 6 9
p(x) 1/6 1/2 1/3

Find and hence .

  1. State and prove multiplication theorem of probability for ‘n’ events.

SECTION –C

 

Answer any TWO questions.                                                           (2×20=40 marks)

 

  1. a) State and prove addition theorem of probability for 3 events.       (10)
  1. b) Three groups of children contain 3 girls and 1 boy; 2 girls and 2 boys; 1 girl and 3 boys respectively. One child is selected at random from each group. Find the chance that the three selected consist of 1 girl and 2 boys. (10)
  1. a) State and prove Baye’s theorem for future events.
  1. b) The probability of x, y and z becoming managers are The probability that the Bonus scheme is introduced if x, y and z become mangers are , and respectively. i) What is the probability that the Bonus scheme will be introduced? ii) If the Bonus scheme has been introduced, what is the probability that the manager appointed was x?
  1. Two dice, one green and the other red are thrown. Let A be the event that the sum of the points on the faces is odd and B be the event that atleast one number is 1.
  1. Define the complete sample space and the events A, B, and
  2. Find the probability of the events:

, ,,

  1. a) State and prove chebychev’s inequality
  1. b) Let the random variable x have the distribution:

.

For what value of p is the var (x) a maximum?

 

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Loyola College B.Sc. Statistics April 2008 Operations Research Question Paper PDF Download

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

NO 29

 

SIXTH SEMESTER – APRIL 2008

ST 6601 – OPERATIONS RESEARCH

 

 

 

Date : 21/04/2008                Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

 

SECTION – A

Answer ALL questions:                                                                                (10 x 2 = 20)

 

  1. Define basic feasible solution and optimal solution in a linear programming problem.
  2. Rewrite into standard form:
  1. What is the role of artificial variables in linear programming?
  2. Write the dual of :
  1. Explain a transshipment problem
  2. What is an unbalanced transportation problem?
  3. Distinguish between CPM and PERT in network analysis.
  4. Define activity and event in network analysis.
  5. Define decision under uncertainity
  6. Give an example of a 3 x 3 game without a saddle point.

 

SECTION – B

Answer any FIVE  questions.                                                                      (5 x 8 = 40)       

 

  1. The standard weight of special type of brick is 5kg and it contains two basic ingredients B1 and B2. B1 costs Rs. 5/kg and B2 costs Rs. 8/kg. The strength considerations dictate that the brick contains not more than 4 kgs of B1 and a minimum of 2 kgs of B2. Find graphically the minimum cost of the brick satisfying the above conditions.
  2. Show that the following linear programming problem has an unbounded solution.
  1. Explain how you will solve a travelling salesman problem.
  2. Draw the network diagram given the following activities and find the critical path.

Job                               :           A         B         C         D         E          F          G        H        I             J         K

Time (days)     :           13        8          10        9          11        10          8        6         7          14       18

Immediate                   –           A         B         C         B         E          D,F      E         H         G,I         J

Predecessor     :

 

  1. Explain the maximal flow problem.

 

  1. Solve the following problem for the minimum time:
I II III IV V
A 16 13 17 19 20
B 14 12 13 16 17
C 14 11 12 17 18
D 5 5 8 8 11
E 3 3 8 8 10

 

 

 

  1. A decision problem is expressed in the following pay-off table (Rs.’ 000s). What is the maximax and maximin payoff action?

 

Strategy

 

State I II III
A – 1880 1840 1800
B – 1620 1600 1640
C – 1400 1420 1720

 

 

 

 

  1. How will you solve a game problem using linear programming?

 

SECTION – C

Answer any TWO   questions.                                                                      (2 x 20 = 40)

 

  1. a) Discuss in brief duality in linear programming (8)
  2. b) Solve using dual simplex method:

 

  1. a) Explain Vogel’s method of finding an initial solution to a transportation problem.      (8)
  1. b) Use least cost method to find initial basic feasible solution and then find the minimum transportation cost for the following problem.

 

Destinations

D1 D2 D3 D4 Supply
01 1 2 1 4 30
Origins 02 3 3 2 1 50
03 4 2 5 9 20
Demand 20 40 30 10 100
  1. a) Explain  i) total float ii) free float and

iii)independent float in network analysis (8)

 

  1. b) The time estimates in weeks for the activities of a PERT network are given below:

 

Activity: 1-2 1-3 1-4 2-5 3-5 4-6 5-6
Opt.time: 1 1 2 1 2 2 3
Most likely time 1 4 2 1 5 5 6
Pessimistic time: 7 7 8 1 14 8 5
  1. Draw the network diagram and find the critical path
  2. Find the expected length and variance of the critical path.
  • What is the probability that the project is completed in 13 weeks? (12)
  1.  a) Explain Laplace and Hurintz criteria in decision theory
  1. b) Solve the following game graphically.

 

 

 

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Loyola College B.Sc. Statistics April 2008 Finan.Ac & Financial Statement Analysis Question Paper PDF Download

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

RO 3

 

B.Sc. DEGREE EXAMINATION – STATISTICS

SECOND SEMESTER – APRIL 2008

CO 2104 / 2101 – FINAN.A/C & FINANCIAL STATEMENT ANALYSIS

 

 

 

Date : 25/04/2008                Dept. No.                                        Max. : 100 Marks

Time : 1:00 – 4:00

 

SECTION A

Answer all questions:                                                              10 x 2 =20 marks

 

  1. Classify the following accounts into Personal, Real and Nominal:
  2. a) Cash account b)  Dividend account    c) Goodwill account
  3. d) Chennai Cricket Club Account

2.a  The subdivisions of a journal into various books are called ___________ books.

  1. A _________ organisation is a legal and accounting entity  whose main     objective’s are to provide        service to the members or beneficiaries.
  2. Give any two advantages of cash flow analysis.
  3. What are Bad debts and how are they treated?
  4. What is imprest system of cash book ?
  5. List out any four direct expenses.
  6. Write short note on Legacy
  7. What is Proprietory fund?
  8. Calculate cost of goods sold: Opening stock – Rs. 2,500, Purchases – Rs.50,000 Closing stock –  Rs. 7000
  9. Compute the Profit or loss on sale of Land: Original cost – Rs. 10,000      Accumulated Depreciation –        5,000  Sale value Rs.5,500.

 

 

SECTION B

Answer any five questions:                                                                 5 x 8 =40 marks

 

11  What is Bank Reconciliation Statement?  Why should it be prepared periodically?

  1. Distinguish between Trial balance and Balance sheet.
  2. Describe the advantages and disadvantages of accounting.
  3. M/s Praveen Furniture Mart purchased the following items during the month of December 2007

5    Purchased from M/s Goodwill furniture

200 Chairs @ Rs. 100 per chair

25 Tables @ Rs. 200 per table

11  Purchased from M/s Nithya motors

One Maruti  car for Rs. 1,40,000

One Scooter for Rs. 14,000

  • Cash purchases from Dilip furniture:

4 Sofa sets @ Rs. 5,000 per set

1 Computer table @ Rs. 2,500

20  Purchased from Ram & Co

24 Dining chairs @ Rs. 200 per chair

4 Dining tables @ Rs. 2,000 per table

Less : 15% trade discount

Prepare purchases book and show ledger posting of purchases book.

  1. From the following balances, prepare the Balance sheet of a Company in the prescribed format, Goodwill       Rs. 1,50,000; Investments Rs. 2,00,000; Share capital Rs. 5,00,000 ;  Reserves Rs. 1,10,000; Share premium           Rs. 15,000; Preliminary expenses Rs. 10,000; Profit and Loss A/c (Cr) Rs. 25,000; Debentures         Rs. 2,50,000, Plant and Machinery  Rs. 2,70,000; Land Rs. 2,00,000; Stock Rs. 80,000; Debtors Rs. 60,000;       Bank balance Rs. 30,000; Unsecured loan Rs. 65,000; Sundry creditors Rs. 35,000

 

  1. From the following Receipts and Payments account of Chennai Club for the year ended 31-3 – 2007.       Prepare Income and Expenditure Account.

Receipts and Payments Account for the year ended 31-3-07

Receipts                      Rs.                Payments                       Rs.

To Balance b/d           3,485               By Books                    6,150

To Entrance fees           650               By Printing and

To Donations             6,000                       Stationery               465

To Subscribtions         6,865               By Newspapers           1,110

To Interest on                                      By Sports Materials    5,000

Investments    1,900               By Repairs                     650

To Sale of furniture        685               By Investments           2,000

To Sale of old                                     By Furniture                1,000

Newspapers       465               By Salary                    1,500

To Proceeds from                                By balance c/d                        3,165

Entertainments     865

To Sundry receipts         125

_____                                                 _______

21,040                                                 21,040

Additional information:

  1. Capitalise Entrance fees and Donations
  2. Sports Materials valued at Rs. 4,000 on 31-3-07.

 

  1. Given the following figures:

Sales                                           Rs. 15,00,000

Gross profit                                20% on sales

Current assets                               4,00,000

Current liabilities                          2,00,000

Fixed assets (Gross) 5,00,000

Less: Depreciation  1,00,000    4,00,000

Calculate : (i)  Capital turnover ratio  (ii) Fixed assets turnover ratio

  • Working capital turnover ratio

 

  1. X Ltd made a profit of Rs. 4,00,000 after considering the following items:

(i)         Depreciation on fixed assets Rs. 15,000

(ii)        Writing off preliminary expenses Rs. 6,000

(iii)       Loss on sale of furniture         Rs.      900

(iv)       Provision for taxation             Rs. 75,000

(v)        Transfer to general reserve      Rs.   5,000

(vi)       Profit on sale of buildings       Rs. 10,000

The following additional information is also supplied to you:

Particulars                   31-12-06                      31-12-07

Rs.                               Rs.

Sundry Debtors                       15,000                         20,000

Sundry Creditors                    12,000                         17,000

Bills receivable                        14,000                         17,500

Bills payable                              9,500                           6,000

Outstanding expenses             3,000                            2,000

Prepaid expenses                         100                               200

You are required to ascertain the amount of cash from operations.

 

SECTION C

Answer any two questions:                                                     2 x 20 =40 marks

 

  1. From the following Trial Balance of Thiru. Raj as on 31st March 2007, Prepare Trading and Profit & Loss A/c and Balance Sheet taking into account the adjustments:

Debit balances         Rs.           Credit balances             Rs.

Land and Buildings          42,000       Capital                         62,000

Machinery                          20,000       Sales                            98,780

Patents                                  7,500       Return outwards              500

Stock 1-4-2006                     5,760       Sundry Creditors          6,300

Sundry debtors                  14,500        Bills payable                  9,000

Purchases                           40,675

Cash in hand                           540

Cash at bank                        2,630

Return inwards                       680

Wages                                  8,480

Fuel and power                    4,730

Carriage on sales                  3,200

Carriage on purchases          2,040

Salaries                               15,000

General expenses                 3,000

Insurance                                 600

Drawings                              5,245

______                                           ______

1,76,580                                         1,76,580

Adjustments

  • Stock on 31-3-2007 was Rs. 6,800
  • Salary outstanding Rs. 1,500
  • Insurance Prepaid Rs. 150
  • Depreciate machinery @ 10% and patents @ 20%
  • Create a provision of 2% on debtors for bad debts.

 

  1. From the following transactions, prepare Three- Column cash book of Akash for the month of Aug 2007

Aug

2007                                                                               Rs.

1       Cash balance                                                   20,000

Bank balance                                                   23,000

3       Paid rent by cheque                                          5,000

4       Cash received on account of cash sales            6,000

6       Payment for cash purchases                              2,000

8       Deposited into bank                                          8,000

9       Bought goods by cheque                                  3,000

10       Sold goods to Naresh on credit                        7,120

12       Received cheque from Mohan                          2,900

Discount allowed to him                                      100

13       Withdrew from bank for office use                  4,350

14       Purchased furniture by cheque                         1,260

15       Received a cheque for Rs. 7,000 from

Naresh in full settlement of his account,

Which is deposited into bank

16       Withdrew for personal use from bank              1,200

18       Suresh our customer has paid directly

Into our bank                                                              4,000

  • Prasad settled his account for Rs. 1,250

By giving a cheque for                                   1,230

  • Prasad’s cheque sent for collection

 

  1. Using the following information, construct a Balance Sheet:

Gross profit (20% on sales)  Rs. 6,00,000

Shareholder’s equity               Rs. 5,00,000

Credit sales to total sales        80%

Total assets turnover(on sales) : 3 times

Average collection period (360 days in a year)  : 18 days

Current ratio                1.6

Long term debt to equity                    40%

 

 

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Loyola College B.Sc. Statistics April 2008 Estimation Theory Question Paper PDF Download

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

           B.Sc. DEGREE EXAMINATION – STATISTICS

NO 24

FIFTH SEMESTER – APRIL 2008

ST 5500 – ESTIMATION THEORY

 

 

 

Date : 28-04-08                  Dept. No.                                        Max. : 100 Marks

Time : 1:00 – 4:00

PART-A

 

Answer ALL the questions:                                                             (10×2=20)

 

  1. Define ‘bias’ of an estimator.
  2. When do you say an estimator is consistent?
  3. Define a sufficient statistic.
  4. What do you mean by bounded completeness?
  5. Describe method of moments in estimation.
  6. State invariance property of maximum likelihood estimator.
  7. Define Loss function and give an example.
  8. Explain ‘prior distribution’ and ‘posterior distribution’.
  9. Explain least square estimation.
  10. Mention any two properties of least squares estimator.

 

PART-B

Answer any FIVE questions:                                                           (5×8=40)

 

  1. If Tn is asymptotically unbiased with variance approaching 0 as , then show that Tn is consistent.
  2. Show that is an unbiased estimate of , based on a random sample drawn from .
  3. Let be a random sample of size n from  population. Examine if is complete.
  4. State and prove RAo-Blackwell theorem.
  5. Estimate by the method of moments in the case of Pearson’s Type III distribution with p.d.f .
  6. State and establish Bhattacharya inequality.
  7. Describe the method of modified minimum Chi square.
  8. Write a note on Baye’s estimation.

 

PART-C

Answer any TWO questions:                                                           (10×2=20)

  1. a) and is a random sample of size 3 from a population with mean value and variance .  are the estimators used to estimate mean value , where  and .
  1. Are T1 and T2 unbiased estimators?
  2. Find the value of such that T3 a consistent estimator?
  • With this value of is T3 a consistent estimator?
  1. Which is the best estimator?
  2. b) If are random observations on a Bernoulli variate X taking the value 1 with probability p and the value 0 with probability (1-p), show that is a consistent estimator of p(1-p).
  1. a) State and Prove cramer-Rao inequality.
  1. b) Given the probability density function

Show that the Cramer-Rao-lower bound of variance of an unbiased estimator of  is 2/n, where n is the size of the random sample from this distribution. [12+8]

  1. a) State and prove Lehmann – Scheffe theorem
  1. b) Obtain MLE of in based on an independent sample of size n. Examine whether this estimate is sufficient for .                   [12+8]
  1. a) Show that a necessary and sufficient condition for the linear parametric function to be linearly estimable is that

ank (A) = rank

where  and

  1. b) Describe Gauss – Markov model [12+8]

 

 

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Loyola College B.Sc. Statistics April 2008 Econometrics Question Paper PDF Download

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

  B.Sc. DEGREE EXAMINATION – STATISTICS

NO 16

 

FOURTH SEMESTER – APRIL 2008

ST 4207/ ST 4204 – ECONOMETRICS

 

 

 

Date : 25-04-08                  Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

SECTION- A

Answer all the questions. Each carries TWO marks.                  (10 x 2 =  20 marks)

 

  1. Define sample space and event of a random experiment.
  2. If P(A) = ¼  , P(B) = ½  and P(AB) = 1/6 , find (i) P(AB) and (ii) P(AcB).
  3. Given:

X= x :    0      1        2        3        4

P(X=x): 1/6  1/8     ¼      1/12    3/8

Find E(2X + 11).

  1. If  f ( x, y) is the joint p.d.f. of X and Y, write the marginals and conditional

distributions.

  1. Write any two properties of expected values.
  2. Define BLUE.
  3. Define the population regression coefficient .
  4. Write variance inflating factor of an estimator in the presence of multicollinearity.
  5. Define autocorrelation.
  6. Define point and interval estimation.

 

SECTION –B

Answer any FIVE questions. Each carries EIGHT marks.                (5 x 8 =  40 marks)

 

  1. Consider 3 urns. Urn I contains 3 white and 4 red , Urn II contains 5 white and 4 red and  Urn III contains 4 white and 4 red balls. One ball was drawn from each urn. Find the probability that  the sample will contain 2 white and 1 red balls.
  2. If a fair coin is tossed 10 times, find the chance of getting (i) exactly 4 heads

(ii) atleast 6 heads (iii) atmost  8 heads (iv) not more than 4 heads.

  1. Derive the least square estimators of the linear model Y = 1  + 2 X + u .
  2. State any six assumptions of the linear regression model.
  3. How to fit a non-linear regression model of the form Y = 1 + 2 X + 3 X 2 ?.
  4. Consider the model Y = 1  + 2 X + u  where X and Y denote respectively

consumer income (hundreds of dollars per person) and consumption of purple

oongs (pounds per person) . The sample size is 20 , sum of X is 300, sum of Y

is 120 , sum of squares of deviations of X from its mean is 500 , sum of product

of deviations of X and Y from their respective means is 66. 5 and sum of squares

of is 3.6.

  • Compute the slope and intercept.
  • Compute the standard error of regression.
  • Compute the standard error of slope.

 

  1. In a book of 520 pages , 390 typo- graphical errors occured. Assuming Poisson

law  for the number of errors per page, find the probability that a random sample

of 5 pages contain (i) no error (ii) atleast 3 errors.

 

 

  1. The mean yield for one-acre plot is 662 kg with a standard deviation of 32 kg.

Assuming normal distribution find how many one-acre plots in a batch of 1000

plots will have yield (i) over 700 kg  (ii) below 65 kg .

 

 

SECTION – C

 

Answer any TWO questions. Each carries TWENTY marks.          (2 x 20 =  40 marks)

 

  1. Consider the following joint distribution of (X,Y):

 

X          0            1            2               3

0        1/27      3/27       3/27           1/27

Y      1        3/27      6/27       3/27              0

2        3/27      3/27        0                  0

3        1/27        0           0                  0

 

(a) Find the marginal distributions of X and Y.

(b) Find E( X ) and V ( X )

(c) Find the correlation between X and Y.

(d) Find E ( Y | X = 2 )

(e) Verify whether or not X and Y are independent.

 

 

  1. (a) Explain the following methods of estimation used in the analysis of regression

models:

(i) Maximum likelihood      (ii) Moments

(b) The heights of 10 males of a given locality are found to be 70 , 67, 62 , 68 , 61

68 ,70 , 64 , 64 , 66 inches. Is it reasonable to believe that the average height is

greater than 64 inches ? Test at 5% significance level.

 

 

 

 

 

 

 

  1. For the following data on consumption expenditure (Y ) , income ( X2 ) and wealth

( X3 ):

 

Y($)   : 70     65      90       95      110      115     120     140      155       150

X2 ($) : 80    100    120     140    160      180      200     220      240       260

X3 ($) : 810  1009  1273   1425  1633    1876    2052   2201    2435     2686

  • Fit a regression model Y = 2 X2 + 3 X3 + u .
  • Find the correlation coefficients between Y and X2 , Y and X3 , X2 and X3.
  • Find unadjusted and adjusted R2 .
  • Test H0 : 2 = 3 = 0 at 5% significance level .

 

  1. (a) For the k-variate regression model Y = 1 + 2 X2 +…+k Xk + u

carry out the procedure for testing  H0 : 2 = 3 = … =  k = 0 against

H1: atleast one k 0.

(b) Write the properties of ordinary least square(OLS) estimators under the

normality assumption.

 

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Loyola College B.Sc. Statistics April 2008 Distribution Theory Question Paper PDF Download

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

NO 19

 

FOURTH SEMESTER – APRIL 2008

ST 4501 – DISTRIBUTION THEORY

 

 

 

Date : 26/04/2008                Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

 

SECTION – A

Answer ALL questions.:                                                                               (10 x 2 = 20)            

 

  1. Explain the joint p.d.f of two continuous random variables X and Y.
  2. Define conditional probability mass function.
  3. Let . Find.
  4. Write down any two properties of negative Binomial distribution.
  5. Define Laplace distribution and find its mean.
  6. Define Beta distribution of first kind.
  7. Define students-t statistic and write down its probability density function.
  8. State the additive property of Chi-square distribution.
  9. Define order statistic and give an example.
  10. Define conditional expectation and conditional variance of a random variable X given Y= y.

 

SECTION – B

Answer any FIVE  questions.                                                                      (5 x 8 = 40)

 

  1. The joint p.d.f of random variables X and Y is given by
  • Find the value of k
  • Verify whether X and Y are independent.
  1. Derive Poisson distribution as limiting form of Binomial distribution.
  2. Define multinomial distribution and find the marginal distributions.
  3. Explain joint distribution function of two dimensional random variable (X,Y) and establish any two of its properties..
  4. Show that for normal distribution mean, median and mode coincide.
  5. Find the MGF of Bivariate normal distribution.
  6. State and prove central limit theorem.
  7. Derive the p.d.f of F-distribution with n1 and n2 degrees of freedom.

 

SECTION – C

Answer any TWO   questions.                                                                      (2 x 20 = 40)

 

  1. a) Obtain mean deviation about mean of Laplace distribution.
  1. b) Show that exponential distribution satisfies lack of memory property.
  1. a) Derive MGF of negative Binomial distribution and show that its mean is less than its variance.
  1. b) Find the factorial moments of hyper-geometric distribution.
  1. a) If X and Y are independent Chi-square variates with n1 and n2 d.f, find the p.d.f of x/x+y.
  1. b) Obtain the MGF. of Binomial distribution with n=7 and p=0.6 and hence find .
  1. a) Let X and Y follow Bivariate normal distribution with and P=0.4. Find the following probabilities.

(i)

(ii)

  1. b) Let X1, X2, …. Xn be a random sample with common p.d.f

Find p.d.f, mean and variance of X(1), the first order statistic.

 

 

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Loyola College B.Sc. Statistics April 2008 Design & Analysis Of Experiments Question Paper PDF Download

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

NO 28

 

SIXTH SEMESTER – APRIL 2008

ST 6600 – DESIGN & ANALYSIS OF EXPERIMENTS

 

 

 

Date : 16/04/2008             Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

 

SECTION – A

Answer ALL the questions:                                                              (10 x 2 = 20)

  1. Define linear contrasts and given an example.
  2. State the assumptions in an analysis of variance.
  3. Write the model representing two-way classified data.
  4. Give a layout for 4 x 4 LSD.
  5. Write all possible treatment combinations in a 23 design.
  6. What do you understand by a missing plot in a design of experiment?
  7. State the advantages of factorial experiments over single factor experiments.
  8. What is confounding?
  9. Define BIBD.
  10. State the parametric relations for the existence of a BIBD.

 

SECTION – B

Answer any FIVE questions:                                                           (5 x 8 = 40)

  1. Discuss the classification of linear models with suitable examples.
  2. Describe two-way classification in analysis of variance.
  3. Give the advantages and disadvantages of randomized block design.
  4. Explain how a missing value is estimated in Latin square design.
  5. Distinguish between complete and partial confounding with illustrations.
  6. Explain confounding in 23 factorial experiment.
  7. Starting with a suitable linear model, obtain intra block analysis of BIBD.
  8. Obtain the efficiency of RBD over CRD.

 

SECTION – C

Answer any  TWO questions:                                                           (2 x 20 = 40)

  1. a) What is random effects model? Give the complete analysis of random effects model.
  2. b) Explain the basic principles of design of experiments. (10+10)
  1. a) Carry out the complete analysis of a CRD.
  1. b) How is the efficiency of a design is measured. Derive the expression to measure the efficiency of a LSD over a RBD. (8+12)
  1. a) Discuss the analysis of a 32 factorial design.
  1. b) Explain the purpose and principle of confounding in factorial experiments. (12+8)
  1. a) With usual parameters a, b, r, k, λ establish the three parametric relation of BIBD.
  1. b) Bring out the significance of recovery of inter-block information in BIBD.

 

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Loyola College B.Sc. Statistics April 2008 Computational Statistics Question Paper PDF Download

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

NO 27

 

FIFTH SEMESTER – APRIL 2008

ST 5503 – COMPUTATIONAL STATISTICS

 

 

 

Date : 06/05/2008                Dept. No.                                        Max. : 100 Marks

Time : 1:00 – 4:00

Answer  all  questions. Each carries 34 marks.

 

1.(a) For the following data:

Commodity                  Base year                              Current  year

Kg.           Rate(RS.)                  Kg.           Rate(RS.)

Rice                        10                 20                            14                  2

Oil                           12                 62                            16                  80

Wheat                      14                10                             18                 19

Ghee                        12                100                           14                 180

Tea                           16                150                           18                 200

Find (i) Laspyre (ii) Paasche (iii)Dorbish-Bowley (iv) Marshall-Edgeworth and (v)Fisher  price and quantity index numbers.(10 marks)

(b) Fit a trend line by the method of least squares for the following data:

Year              : 1994  1995   1996  1997  1998  1999  2000  2001  2002  2003

Sales(Crores):   12      14       18      20      26     25      30      32      38       42

Also estimate the trend values for the years from 2004 to 2010.Further compute 3 year

and 4 year moving averages.(14 marks)

(c) The following figures show the distribution of digits in numbers chosen at random

from a telephone directory:

Digits       :  0         1         2         3         4        5         6        7        8       9

Frequency: 1026  1107   997     966    1075   933    1107   972    964   853

Test whether the digits may be taken to occur equally frequently in the directory.Use

.05 level of significance.(10 marks)

[OR]

(d) Identify the monthly seasonal indices for the 3 years of expenses for a six-unit

apartment house in southern Florida as given here.Use a 12-month moving average

calculation.

Expenses

        Month                 Year1             Year2       Year3

January                170                  180            195

February             180                  205            210

March                 205                  215            230

April                    230                  245            280

May                     240                  265            290

June                     315                  330            390

July                     360                  400            420

August                             290                  335            330

September           240                  260            290

October                            240                  270            295

November                        230                  255            280

December            195                  220            250    (20 marks)

(e)The following table gives probabilities and observed frequencies in four classes AB,Ab,aB and ab in a genetical experiment. Estimate the parameter  by the method of maximum likelihood and its standard error.

 

Class                        Probability                   Observed frequency

AB                               ¼(2+)                                108

Ab                               ¼(1-)                                   27

aB                               ¼(1-)                                   30

ab                               ¼ ()                                       8        (14 marks)

 

2(a) The National Association of Home Builders provided data on the cost of the most

popular home remodeling projects.Sample data on cost in thousands of dollars for

two types of remodeling projects are as follows.

 

 

Kitchen                    Master Bedroom

 

  • 0
  • 9
  • 4
  • 8
  • 9
  • 8
    • 6
    • 0

21.8

23.6

Develop a 95% confidence interval for the difference between the two Population means.                                                                                                                                                                (10 marks)

(b)Two independent samples of 8 and 7 items respectively had the following values:

Sample1: 9       11        13        11        15        9          12        14

Sample2: 10     12        10        14        9          8          10

Is the difference between the means of samples significant ? Test at 1% level of  significance .                                                                                                                                                                    (14 marks)

(c) The Dow Jones Industrial Average varies as investors buy and sell shares of the

30 stocks that make up the average.Samples of  the Dow Jones Industrial Average

taken at different times during the first 5 days of November 1997 and the first 5

days of December 1997 are as follow:

November           December

  • 8066
  • 8209
  • 7842
  • 7943
  • 7846
  • 8071
  • 8055
  • 8159
  • 7828
  • 8109

Using a .05 level of significance, test to determine whether the population variances for

the two time periods are equal. (10 marks)

[or]

(d) Fit a Poisson distribution to the following data and test the goodness of fit:

No.of accidents:  0           1          2          3          4          5          6

No. of days      :  150       65        45        34        10        6          2  (14 marks)

 

(e) One of the questions on the Business Week 1996 Subscriber Study was ,”In the past

12  months ,when travelling for business, what type of airline ticket did you purchase

Most often ?” The data obtained are shown in the following contingency table.

Type of Flight

——————-

Type of Ticket                            Domestic Flights            International Flights

First class                                                29                                 22

Business/executive class                         95                                 121

Full fare economy/coach class                518                               135

Using=.05 ,test for the independence of type of flight and type of ticket.(10 marks)

 

(f)     A test was conducted of two overnight mail delivery services. Two samples of

identical deliveries were set up so that both delivery services were notified of the

need for a deliveryat the same time.The hours required to make each  delivery

follow. Do the data shown suggest a difference in the delivery times for the two

services ? Use Wilcoxon signed ranks for the test at 5% significance level.   The

data follows:

Service

————————–

Delivery                                1                      2

1                                      24.5                 28.0

2                                      26.0                 25.5

3                                      28.0                 32.0

4                                      21.0                 20.0

5                                      18.0                 19.5

6                                      36.0                 28.0

7                                      25.0                 29.0

8                                      21.0                 22.0

9                                      24.0                 23.5

10                                     26.0                 29.5

11                                     31.0                 30.0  (10 marks)

 

3 (a) Consider a population of  6 units with values : 2, 5, 8, 11,13 and 14

[i] Write down all possible samples of size 2 without replacement from this population

[ii] Verify that the sample mean is an unbiased estimate of the population mean

[iii] Calculate  the Sampling variance and verify   that it agrees with the  variance of

the sample mean under SRSWOR.

[iv]  Also , Verify that  the Sampling Variance is less than the variance of  the sample

mean which is obtained from SRSWR.                                                          [14]

(b) The data given below is   for a small  sheep population which exhibits  a steady rising  trend. Each column represents a systematic sample and rows represent the strata.

[i] Calculate sampling variance under systematic sampling

[ii] Calculate sampling variance under stratified  sampling

[iii] Calculate sampling variance for without stratification and without replacement

[iv] Compare the precision.

Sample Number

Stratum #

 1 2 3 4
I 5 7 9 11
II 8 11 14 14
III 9 13 15 17
IV 11 14 17 21

[20]

[OR]

[c] The table given below shows the summary of data for Paddy crop census of all the

2500 farms in a state. A sample of 125 farms is to be selected from this population

The farms were stratified according to farm size(in acres)  into 4 strata as given below:

            Stratum

Number

 Farm

Size

(inacres)

 No. of

Farms Ni

 Average area Under paddy crop (in acres) per farm

ŸNi

 Standard

Deviation

si
1 0-100 600 45 8
2 101-200 900 105 12
3 200-500 700 130 20
4 >500 300 180 40

[i] Estimate the total area under Paddy cultivation for the state

[ii] Find the sample sizes of each stratum under proportional allocation.

[iii] Find the sample sizes of each stratum under Nayman’s Optimum allocation

[iv] Calculate the variance of the estimated total area under Proportional allocation

[v] Calculate the variance of the estimated total area under Nayman’s Optimum allocation

[vi] Calculate the variance of the estimated total area under un-stratified simple

random sampling without replacement.

[vii] Estimate  gain in efficiency resulting from [iv] and [v] and compare them with [vi].            [34]

 

 

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Loyola College B.Sc. Statistics April 2008 Basic Sampling Theory Question Paper PDF Download

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

           B.Sc. DEGREE EXAMINATION – STATISTICS

NO 13

THIRD SEMESTER – APRIL 2008

ST 3502/ 4500 – BASIC SAMPLING THEORY

 

 

 

Date : 29-04-08                  Dept. No.                                        Max. : 100 Marks

Time : 1:00 – 4:00

 

SECTION – A

Answer ALL questions:                                                       (10×2=20)

  1. In what situations sampling is inevitable?
  2. How would you distinguish between estimate and estimator?
  3. Differentiate between SRSWR and SRSWOR.
  4. Define standard error of an estimator.
  5. Explain pps sampling.
  6. Explain cumulative total method of selecting pps sampling.
  7. What do you understand by stratified random sampling?
  8. Distinguish between systematic sampling and stratified random sampling.
  9. What is circular systematic sampling?
  10. What are the advantages of systematic sampling?

 

SECTION-B

Answer any FIVE questions:                                                           (5×8=40)

  1. Explain the principles of sampling methods.
  2. In SRSWOR, prove that sample mean is an unbiased estimator of the population mean and its sampling variance is given by .
  3. Explain the various types of allocations used in stratified random sampling method.
  4. Find the relative precision of systematic sample mean with simple random sample mean.
  5. A village has 10 holdings consisting of 50, 30, 45, 25, 40, 26, 24, 35, 28 and 27 fields. Select a sample of size 4 by using Lahiri’s method.
  6. Explain sampling and non sampling errors.
  7. Derive the formulae for the mean and variance of systematic sample..
  8. Distinguish between probability and non-probability sampling and write down their advantages and disadvantages.

 

SECTION – C

Answer any TWO questions:                                                           (2×20=40)

  1. a) Describe Lahiri’s method of selection and it’s merits over cumulative method.
  1. b) A random sample of size n=2 was drawn from a colony of 5 households having monthly income as follows:

Household:      1          2          3          4          5

Income(Rs):    156      149      166      164      155

  • Calculate population mean and population variance .
  • Enumerate all possible samples of size 2 by the replacement method and show that the sample mean gives an unbiased estimate of the population mean and find its sampling.

Variance: Also show that s2 is an unbiased estimate of the population variance .

  1. a) Show that under fixed cost.
  1. b) Compare the variances of the sample mean under systematic sample with stratified and simple random sampling, assuming linear trend.
  1. a) Explain different systematic sampling schemes.
  1. b) Derive the variance of Hansen-Hurwitz estimator for population total.
  1. a) Show that in SRSWOR the probability of selecting a sample of size ‘n’ from ‘N’ units is 1/Ncn.
  1. b) In a bank there are 5000 deposit accounts. A random sample of 50 accounts was drawn WOR and the following information was obtained and . Where Yi denotes the amount in a deposit account. Find an unbiased estimate of the average amount in a deposit account and find its estimated variance.

 

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Loyola College B.Sc. Statistics April 2008 Applied Stochastic Processes Question Paper PDF Download

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

NO 20

 

FIFTH SEMESTER – APRIL 2008

ST 5400 – APPLIED STOCHASTIC PROCESSES

 

 

 

Date : 05/05/2008                Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

SECTION A

Answer ALL the questions

Each question carries 2 marks (10 X 2 =20 Marks)

 

1)   Explain continuous time Markov Chain.

2)   Give an example for discrete time Markov Chain.

3)   Define Poisson Process.

  • Define recurrent state of a Markov Chain and give an example.
  • What is renewal process?
  • Define a pure birth process.
  • Define a renewal counting process.

8)   Give an example of a Martingale.

9)   Give an example of a renewal process.

10) State renewal theorem.

SECTION B

Answer any 5 questions

Each question carries 8 marks (5  X 8 = 40 Marks)

 

  • How do you relate the consumer’s brand switching behavior to a Stochastic model?
  • Relate any queuing model to a discrete parameter space and discrete state space

stochastic model.

  • Relate the time sharing computer system to a stochastic model.
  • Explain one dimensional random walk.
  • Suppose that the probability of a dry day (state 0) following a rainy day (state 1) is 1/3

and the probability of a rainy day following a dry day is  ½  . Here we have two state Markov chain.  (i) Find the transition  probability matrix (ii) Given that October 1 is a dry day what is the probability that October 3 is a dry day and October 5 is a dry day.

 

  • A rat is put in to the maze as shown below. The rat moves through the compartments

at random. If there are k ways to leave the compartment he chooses each of these with probability 1/k. He makes one change of compartment at each instant of time. The state of the system is the number of compartment the rat is in. Determine the transition probability matrix.

 

 

17)  Explain the following processes with examples

  1. Counting Process
  2. Markov Process (Each carries 4 Marks)

 

 

 

18) Let Y0 = 0, Y1 , Y2 ,Y3 , …be independent rv’s with E( |Yn | ) < , for all n and

E(Yn ) = 0 , for all n. If X0 = 0 and Xn = Show that { Xn } is a martingale with

respect to { Yn }.

 

 

SECTION C

Answer any 2 questions

Each question carries 20 marks (2  X 20 = 40 Marks)

 

19) Let {X(t), t0} be a Poisson process. Find the distribution of X(t).

20 a )   Find the periodicity of the Markov Chain with the state space {0,1,2,3} and the

transition probability matrix

 

P =

 

20 b) Let {Xn ,n=0,1,2,3,…} be a sequence of iid rv’s with common probability

P(X0 = i ) = pi , i = 0, 1, 2,… Show that  {Xn ,n=0,1,2,3,…} is a Markov chain.

 

21 a) Let { Xt ,t e T) be a process with stationary independent increments when

T = {0,1,2,…}. Show that the process is a Markov process.

 

21 b) Consider the Markov chain with state space S={0,1,2,3,4} and one step Transition

probability matrix

 

 

Find the equivalence class and periodicity of states.

 

22) Explain the following in detail in the context of the appropriate applied scenario.

( Each Carries 5 Marks)

  1. Stochastic Processes with discrete parameter and discrete state space.
  2. Stochastic Processes with discrete parameter and continuous state space.
  3. Stochastic Processes with continuous parameter and discrete state space.
  4. Stochastic Processes with continuous parameter and continuous state space.

 

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Loyola College B.Sc. Statistics April 2008 Applied Statistics Question Paper PDF Download

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

NO 26

 

FIFTH SEMESTER – APRIL 2008

ST 5502 – APPLIED STATISTICS

 

 

 

Date : 03/05/2008                Dept. No.                                        Max. : 100 Marks

Time : 1:00 – 4:00

 

SECTION – A      ( 10 x 2 = 20 Marks)

Answer ALL questions.

 

  1. What is an index number? What are its uses?
  2. What is meant by splicing an index number?
  3. Define a Time series and give examples.
  4. Describe semi-average method of measuring trend.
  5. Define crude and specific death rates.
  6. Define Pearle’s Vital index in the measurement of population growth.
  7. Define partial correlation coefficient.
  8. Give a formula for multiple correlation coefficient R1.23.
  9. What is meant by Economic Census?
  10. Write a note on live stock statistics.

 

 

SECTION – B     (5 x 8 = 40 Marks)

Answer any FIVE questions.

 

  1. Discuss the steps involved in the construction of cost of living index number.
  2. The prices of six commodities in the years 2001 and 2005 are given below.  Compute the price index based on price relatives using the arithmetic mean.

 

 

Commodity
Year A B C D E F
2001 90 120 40 100 170 240
2005 110 140 60 150 180 260

 

  1. What are the components of time series? Explain them.
  2. Compute the linear trend by the method of least squares given the following data.  Estimate the trend for the year 2009.

 

Year 2002 2003 2004 2005 2006 2007
Sales(Lakhs) 75 83 109 129 134 148

 

  1. Describe the components of a Life Table.
  2. Explain the Gross and Net Reproduction Rates.
  3. Discuss the functions of National  Sample Survey Organisation.
  4. Given the values of  r12=0.8, r13=0.6 and r23=-0.7, compute the values of r23.1 and r13.2.

 

 

 

 

 

SECTION-C     (2 x 20 = 40 Marks)

Answer any TWO questions.

 

  1. (a). What are the properties to be satisfied by a good index number?  Explain them in detail.

(b). The index numbers for the years from 1992 to 2002 are given below.  Compute the chain base index numbers.

 

Year 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002
Index 100 120 122 116 120 120 137 136 149 156 137

 

  1. (a). Discuss various methods of measuring Seasonal indices in Time series.

(b). The following table gives the prices of a spare part of a car for the period of five years.  Using the method of Link relatives, compute the Seasonal indices.

 

Quarter/Year 1990 2000 2001 2002 2003
I 30 35 31 31 34
II 26 28 29 31 36
III 22 22 28 25 26
IV 31 36 32 35 33

 

  1. (a). Compute the General Fertility Rate, Specific Fertility Rate, Total Fertility Rate and the Gross Reproduction Rate from the following table.

 

 

Age group of Child bearing females 15-19 20-24 25-29 30-34 35-39 40-44 45-49
Number of women(‘000) 16.0 16.4 15.8 15.2 14.8 15.0 14.5
Total births 260 2244 1894 1320 916 280 145

 

 

(b). In the usual notation, derive the multiple regression equation of X1 on X2 and X3.

 

  1. (a). Write short notes on shifting and deflating index number.

(b). Discuss the methods of National Income estimation.

(c). Given the age returns for the two ages x=9 years and x+1=10 years with l9=75,824, l10=75,362, d10=418 and T10=49,53,195, complete the entries of the life table for the two ages.

 

 

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Loyola College B.Sc. Statistics Nov 2008 Testing Of Hypothesis Question Paper PDF Download

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

BA 11

 

FIFTH SEMESTER – November 2008

ST 5501 – TESTING OF HYPOTHESIS

 

 

 

Date : 05-11-08                     Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

PART – A

 

Answer ALL the Questions.                                                                               (10 x 2 =20 marks)

 

  1. Define : Best Critical Region
  2. What are randomized tests? Give an example of randomized test.
  3. Give an example of a family of density functions not having MLR Property.
  4. When do you say a density function is a member of one parameter exponential family?
  5. What is the fundamental difference between SPRT and other conventional tests?
  6. Describe: Likelihood ratio criterion.
  7. Mention the statistic used for testing the hypothesis that the population correlation coefficient is zero.
  8. Define Confidence level.
  9. Define the term run in connection with Non-parametric methods
  10. What is Empirical Distribution Function?

 

 

PART – B

 

Answer any FIVE questions.                                                                             (5 x 8 =40 marks)

 

  1. State and prove Neyman Pearson lemma
  2. Show that Binomial densities are members of one parameter exponential family.
  3. Derive the UMPT test of level 0.05 for testing the hypothesis against the alternative based on a single observation drawn from exponential distribution with mean and also obtain its power function
  4. Derive the likelihood ratio test for testing  againstbased on a sample of size 17 drawn from when is unknown.
  5. Write a descriptive note on SPRT
  6. Derive the large sample confidence interval for in the case of exponential distribution with mean
  7. Explain run test for randomness.
  8. Describe Kolmogrov-Smirnov one sample test

 

 

 

PART – C

 

Answer any TWO questions.                                                                             (2 x 20 =40 marks)

 

  1. Derive the MPT of level 0.10 for testing against the alternative in Poisson distribution with mean  based on a sample of size 10 and compute the power of the test.

 

  1. Derive the UMPT for testingagainst based on a sample of size n drawn from and also derive its power function.

 

  1. Derive the likelihood ratio test for testing the equality of two normal population means assuming that the variances are unknown but equal and the sample sizes are different.

 

 

  1. Write short notes on the following:
  • Randomised tests vs Nonrandomised tests
  • Monotone Likelihood Ratio Property
  • Large sample confidence intervals
  • Mann-Whitney U Test

 

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Loyola College B.Sc. Statistics Nov 2008 Statistical Mathematics – II Question Paper PDF Download

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

BA 07

 

THIRD SEMESTER – November 2008

ST 3500 – STATISTICAL MATHEMATICS – II

 

 

 

Date : 06-11-08                     Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

 

SECTION – A

Answer ALL the Questions                                                                    (10 x 2 = 20 marks)

 

  1. Define lower sum of a function corresponding to a partition of an interval [a, b].
  2. State the linearity property of Riemann integrals.
  3. Define probability density function (p.d.f.).
  4. What is an improper integral? Give an example.
  5. Define absolute convergence of an improper integral.
  6. Is the integral  dx convergent or divergent?
  7. Change the order of integration in the double integral
  8. Define a symmetric matrix.
  9. Show that inverse of a non-singular matrix is unique.
  10. Define characteristic root and vector of a matrix.

 

SECTION – B

Answer any FIVE Questions                                                                  (5 x 8 = 40 marks)

 

  1. If P  is any partition of [a, b], show under usual notations that

m ( b – a) ≤ L (P , f ) ≤ U(P , f ) ≤ M ( b – a)

 

  1. Show that if f is R-integrable on [a, b], then | f | is integrable on [a, b].

 

  1. If f(x) = cx , 0 < x < 1, is a p.d.f. find ‘c’ and the mean and variance of the distribution.
  2. Discuss the convergence of the improper integral  dx (where a > 0) by varying ‘p’.

 

  1. Evaluate ∫ ∫ xy dy dx over the positive quadrant of the circle x2 + y2 = a2

 

  1. Define moment generating function of a bivariate distribution. Show how the means, variances and covariance can be found from it.

 

  1. If λ is the characteristic root of a matrix A, show that λn is a characteristic root of An and both have the same associated characteristic vector. Also, show that one can always find a normalized (unit) characteristic vector associated with a characteristic root.

 

  1. Define (i) Hermitian matrix, (ii) Idempotent matrix, (iii) Scalar matrix,    (iv) Orthogonal matrix

 

 

 

 

 

SECTION – C

Answer any TWO Questions                                                                 (2 x 20 = 40 marks)

 

  1. State and prove the First and Second Fundamental Theorems of Integral Calculus.

 

  1. (a) State and prove the Comparison Test for convergence of an improper integral of any one kind.

(b) Test the convergence of the integrals: (i)  dx  (ii)  dx          

(10 +10)

 

  1. Let f(x, y) = x + y, 0 < x, y < 1, be the joint p.d.f. of (X, Y). Find the joint distribution function. Also, find the means, variances and covariance.

 

  1. (a) State and prove Cayley-Hamilton Theorem.

(b) Find the inverse of the following matrix using the above theorem:

(10 +1 0)

 

 

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Loyola College B.Sc. Statistics Nov 2008 Statistical Methods Question Paper PDF Download

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

   B.Sc. DEGREE EXAMINATION – STATISTICS

BA 01

 

FIRST SEMESTER – November 2008

ST 1500 – STATISTICAL METHODS

 

 

 

Date : 10-11-08                     Dept. No.                                        Max. : 100 Marks

Time : 1:00 – 4:00

 

PART – A                                 (10×2=20)

Answer ALL the questions

  1. What is a census survey?
  2. Identify the scale used for each of the following variables
    1. Calories consumed during the day.
    2. Marital status.
    3. Perceived health status reported as poor, fair, good or excellent.
    4. Blood type
  3. Mention any four measures of dispersion.
  4. Give a measure of kurtosis.
  5. State the principle of least squares.
  6. What is the standard form of growth curves?
  7. When will the regression lines be perpendicular to each other?
  8. If the regression coefficients are b­XY­ = – 0.4 and b­YX­ = – 0.9 find the

correlation coefficient between X and Y.

  1. What is a dichotomous classification?
  2. State the relation between Yule’s coefficient of association and

coefficient of colligation.

 

PART – B                                 (5×8=40)

Answer any FIVE questions

  1. Describe any two methods of collecting primary data along with their

merits and demerits.

  1. Explain the importance of diagrammatic representation of data.
  2. Compute mean and median for the following frequency distribution

Sales target : 10-20     20-30     30-40     40-50     50-60

(Rs.lakhs)

No. of times

achieved  :    6             8           12             9             5

  1. The sum and sum of squares corresponding to length X (in cm) and weight Y (in gms) of 50 tapioca tubers are given below:

∑X = 212, ∑X­­2 = 902.8, ∑Y = 261, ∑­Y­2 = 1457.6

Which is more varying, the length or weight?

  1. Measurements of serum cholesterol (mg/100ml) and arterial calcium deposition (mg/100g dry weight of tissue) were made on 12 animals. The data are as follows:

Calcium

(X)  :  59    52    42    59    24    24    40    32    63    57    36    24

Cholesterol

(Y)  : 298  303  233  287  236  245  265  233  286  290  264  234

Calculate the correlation coefficient.

 

 

 

  1. The equations of the two regression lines obtained in a correlation

analysis are as follows:

3X+12Y = 19, 3Y+9X = 46

Obtain i) the value of correlation coefficient.

  1. ii) Mean values of X and Y.

iii) Ratio of the coefficient of variability of X to that of Y.

  1. What do you understand by consistency of given data? Examine the

consistency of the following data:

N = 1000, (A) = 600, (B) = 500, (AB) = 50, the symbols having their

usual meanings.

  1. In a certain investigation carried on with regard to 500 graduates and 1500 non-graduates, it was found that the number of employed graduates was 450 while the number of unemployed non-graduates was 300.

In the second investigation 5000 cases were examined. The number of

non-graduates was 3000 and the number of employed non-graduates was

  1. The number of graduates who were found to be employed was
  2. Calculate the coefficient of association between graduates and

employment in both the investigations. Can any definite conclusion be

drawn from the coefficients?

PART – C                                 (2×20=40)

Answer any TWO questions

 

  1. Draw a Histogram for the following frequency distribution of output produced by 190 workers in a firm and use it to find an approximate value of the mode. Also verify it using the formula.

Output in units : 300-310   310-320   320-330   330-340   340-350

No. of workers :      9              20             24            38            48

Output in units : 350-360   360-370   370-380

No. of workers :    27              17             7

  1. Calculate a measure of dispersion and a measure of skewness based on quartiles from the following distribution:

Wages (Rs.): below 35    35-37    38-40    41-43    over 43

No.of wage

earners    :        14          60         95          24            7

  1. Consider the following data where x is temperature (in oc) and Y is the number of eggs per cm­2 .

X   :   3        5       8        14       21      25      28

Y   : 2.8     4.9     6.7     7.6      7.2     6.1     4.7

Fit a quadratic equation to these data.

  1. Various dose of a poisonous substance were given to groups of 25 mice and the following results were observed:

Dose(mg):  4      6      8      10      12      14      16

Number

of deaths:   1     3       6      8       14      16      20

Find the equation of the regression lines. Estimate the number of deaths

in a group of 25 mice who receive a 7-milligram dose of this poison.

 

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