B.Sc Corporate Statistics Question Paper 2006

Loyola College B.Sc. Statistics April 2006 Testing Of Hypothesis Question Paper PDF Download

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             LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

AC 19

FIFTH SEMESTER – APRIL 2006

                                                    ST 5501 – TESTING OF HYPOTHESIS

(Also equivalent to STA 506)

 

 

Date & Time : 22-04-2006/1.00-4.00 P.M.   Dept. No.                                                       Max. : 100 Marks

 

 

PART – A

Answer all the questions.                                               (10 x 2 = 20 Marks)

 

  1. Define a simple and composite hypothesis.
  2. Distinguish between a randomized and non-randomized test.
  3. Provide the form of one-parameter exponential family.
  4. When a test of hypothesis is called uniformly most powerful?
  5. Define likelihood ratio test.
  6. What is a sequential probability ratio test?
  7. Write two uses of chi-square distribution in tests of significance.
  8. Write the 95% confidence interval for the population mean based on large sample.
  9. Define the concept of a quantile of a distribution of a random variable of the continuous type.
  10. Write a note on the sign test.

 

PART – B

Answer any Five questions.                                                       (5 x 8 = 40 Marks)

  1. If X1 X2 …..Xn is a random sample from N (q, 1) ,  q Î R , find a most powerful test for testing H0 : q = 0 against H1 : q = 1.
  2. Let X1 X2 …..X10 denote a random sample of size 10 from a Poisson distribution with mean q. Show that the critical region C defined by  is a best critical region for testing H0: q = 0.1 against H1 : q = 0.5.  For this test determine the significance level   a and the power at  q = 0.5.
  3. X1 X2 …..X25 denote a random sample of size 25 from a normal distribution

N (q, 100).  Find a uniformly most powerful critical region of size a = 0.10 for testing H0: q  = 75 against H1: q > 75.

 

  1. Let Y1 < Y2 < …. < Y5 be the order statistics of a random sample of size n =5 from a distribution with p.d.f

f (x; q) = ½  e– |x– q|,   x Î R, for all real q.  Find the likelihood ratio test for testing Ho : q = q0 against H1 : q ¹ q0.

 

  1. Let X be N (0, q) and let q¢ = 4, q¢¢ = 9, a0 = 0.05 and b0 = 0.10. Show that the SPRT can be based upon the statistic .  Determine c0 (n) and c1 (n).

 

  1. A random sample of 100 units was drawn from a large population. The mean and standard error of the sample are respectively 45 and 8.   Obtain 95% confidence interval for the population mean.

 

  1. For the following data:

X1  :        25        30        45        52        65        75        80        42        50        60

X2 :         60        40        35        50        60        72        63        40        55        62

Test whether the two population variances are equal.  Use 5% significance level.

 

  1. Let X denote the length of time in seconds between two calls entering a college switch board. Let p denote the unique median of this continuous type distribution.  Test H0: p = 6.2 against H1: p < 6.2 based on a random sample of size 20.

 

6.8          5.7       6.9       5.3       4.1       9.8       6.7       7.0       2.1       19.0     18.9

16.9        10.4     44.1     2.9       2.4       4.8       18.9     4.8       7.9

 

PART – C

Answer any Two questions.                                           (2 x 20 = 40 Marks)

 

  1. (a) State and prove Neyman – Pearson theorem.

(b) If  X1 X2 …..Xn  is a random sample from a distribution having p.d.f. of the form f (x; q) = q xq–1,  0 < x < 1, zero elsewhere, show that a best critical region for testing Ho: q = 1 against H1: q = 2 is C = {(x1, x2,…..xn)  :                                     (10+10)

 

  1. Let X1 X2 …..Xn be a random sample from N (q1, q2) and let
    W = {(q1, q2) : –¥ < q1 < ¥, 0 < q2 < ¥} and w = {(q1, q2) : q1 = 0, 0 < q2 < ¥)}.

Perform the likelihood ratio test for testing H0: q1 = 0, q2 > 0            against H1: q1 ¹ 0,
q2 > 0.

  1. (a) Consider the following data:

X:        32        40        50        62        70        35        42        45        19        30

Y:           30        43        55        60        65        23        32        40        20        35

Test whether the two population means are equal at 1% significance level.

 

  • The number of transactions in a teller’s counter during the days of the week is given below:

Mon.             Tue.                 Wed.               Thu.                 Fri.                   Sat

33                 28                    24                    22                    30                    19

Test whether the number of transactions are uniformly distributed or not.  Use 1% level of significance.                                                                                                                    (10+10)

 

  1. Let X and Y denote the weights of ground cinnamon in 120 gram tins packaged by companies A and B respectively. Use Wilcoxon test to test the hypothesis
    H0 : px = py against H0 : px < py.  The weights of n1 = 8 and n2 = 8 tins of cinnamon packages by the companies A and B selected at random yielded the following observations of X and Y respectively.

X:  117.1       121.3        127.8        121.9          117.4       124.5      119.5        115.1

Y:  123.5       125.3        126.5        127.9          122.1       125.6      129.8        117.2

 

 

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Loyola College B.Sc. Statistics April 2006 Statistical Process Control Question Paper PDF Download

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             LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

AC 24

SIXTH SEMESTER – APRIL 2006

                                           ST 6602 – STATISTICAL PROCESS CONTROL

(Also equivalent to STA 602)

 

 

Date & Time : 24-04-2006/9.00-12.00         Dept. No.                                                       Max. : 100 Marks

 

 

Section A

 

Answer all questions                                                                         ( 10 ´ 2 = 20 )

 

  1. What are the chief aspects of quality?
  2. What are quality costs?
  3. What is the difference between conformity and non – conformity?
  4. Mention any two ways of detecting the stability of a process using control charts.
  5. What is the ARL for a process that is in – control? How is it interpreted?
  6. What are ‘Specification Limits’?
  7. Mention the difference between c – chart and u – chart.
  8. Mention the advantage of acceptance sampling plan procedures.
  9. What is the use of probability plots?
  10. Give the control limits for EWMA control chart.

 

Section B

Answer any five  questions                                                               ( 5 ´ 8 = 40 )

 

  1. Draw the phase diagram of quality improvement and explain it.
  1. What are 3 sigma limits? Explain the logic behind their usage in control charts.
  2. The number of nonconforming switches in samples of size 150 is shown below. Construct a fraction nonconforming control chart for these data. Does the process appear to be in control? If not, assume that assignable causes can be found for all points outside the control limits and calculate the revised control limits.

Sample number:1        2          3          4          5          6          7          8

Number of

Nonconforming

Switches          :8         1          3          0          2          4          0          1

 

Sample number:9        10        11        12        13        14        15

Number of

Nonconforming

Switches          :10       6          6          0          4          0          3

  1. A control chart is to be established on a process producing refrigerators. The inspection unit is one refrigerator and a control chart for nonconformities is to be used. As preliminary data, 16 nonconformities were counted in inspecting 30 refrigerators.
    • What are the 3 – sigma control limits?
    • What is the probability of Type I error for this control chart?
    • What is the probability of Type II error for this control chart?
    • Find the average run length if the number of defects is actually 2.
  2. Explain the different approaches in the construction of u – chart with variable sample size.
  3. Explain the procedure for constructing a cumulative sum control chart.
  4. What is meant by acceptance sampling? Mention its advantages.
  5. Derive an expression for ‘Average Outgoing Quality’ with reference to single sampling plan.

Section C

Answer any two  questions                                                               ( 2 ´ 20 = 40 )

 

  1. a.) Explain the role of designed experiments in quality improvement.

b.) The data below represent the results of inspecting all units of a personal computer produced for the last 10 days. Construct a standardized

fraction nonconforming control chart for these data. Does the process appear to be in control? If not, find the revised control limits.

Day:1     2     3     4     5     6     7     8     9     10

Units Inspected:80  110 90  75   130  120 70   125  105 95

Nonconforming

Units:4     7     5    8     6      6     4      5      8     7               (8+12)

  1. ) Explain the statistical basis of a p – chart and derive its control limits.

b.) Construct probability plot to verify whether the following data has been generated from a normal population.

15,10,18,20,22,14,16,17.                                                        (10+10)

 

  1. ) Derive the control limits for and R chart.

b.) Bath concentrations are measured hourly in a chemical process. The following data shows the concentration observed on the past 10 days each on a 4 hourly period.

Day                             Concentration

1                      160      186      190      206

2                      158      195      189      210

3                      150      179      185      216

4                      151      184      182      212

5                      153      175      181      211

6                      154      192      180      202

7                      158      186      183      205

8                      162      197      186      197

9                      169      205      185      188

10                    173      203      187      183

Analyze the data using the cumulative – sum control chart if the target mean concentration is 170.                                                                            ( 10 + 10 )

 

  1. a) What are rectifying inspection plans? Mention its advantages.

b)Consider a single sampling plan with n = 100 , c = 2. Find the OC function corresponding to the incoming lot fraction defective p = 0.05 , 0.10 , … , 0.30

( 10 + 10 )

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Loyola College B.Sc. Statistics April 2006 Operations Research Question Paper PDF Download

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             LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

AC 23

SIXTH SEMESTER – APRIL 2006

                                                    ST 6601 – OPERATIONS RESEARCH

(Also equivalent to STA 601)

 

 

Date & Time : 21-04-2006/9.00-12.00         Dept. No.                                                       Max. : 100 Marks

 

 

SECTION A  (10 x 2 =20)

Answer ALL the questions.  Each carries two Marks

  1. Define saddle point of a pay-off matrix
  2. How many basic cells will be there in a starting solution where there are 4 destinations and 3 origins in a transportation problem ?
  3. Distinguish between “pure” and “mixed” strategies
  4. What is a minimal spanning tree ?
  5. How do you identify the critical activities of a project ?
  6. Give the formula for free float and total float corresponding to an activity defined by arcs i and j
  7. How will you conclude the presence of more than one optima for an LPP ?
  8. What is an unbalanced transportation problem ?
  9. Give the fundamental difference between PERT and CPM
  10. In what way Floyd’s algorithm is superior to Dijkstra’s algorithm ?

 

SECTION B (5 x 8 =40)

Answer any FIVE of the following. Each carries EIGHT marks

  1. Diamond is an aspiring young student of Loyola College. He realizes that “all work and no play makes him a dull boy”. As a result, Diamond wants to apportion his available time of about 10 hours a day between work and play. He estimates that play is twice as much fun as work. He also wants to study at least as much as he plays. However, Diamond realizes that if he is going to get all his homework assignments done, he can not play more than 4 hours a day. How should Diamond allocate his time to maximize his pleasure from both work and play ?

 

  1. Comment on the solution of the following LPP

Maximize

Subject to

 

 

 

  1. Specify the range for value of the game in the following case assuming that the payoff is for player A

B1 B2       B3       B4

 

A1       1          9          6          0

 

A2       2          3          8          4

 

A3       -5         -2         10        -3

 

A4       7          4          -2         -5

 

  1. Use the Hungarian method to solve the following Assignment Problem

 

$3  $9        $2        $3        $7

 

$6  $1        $5        $6        $6

 

$9  $4        $7        $10      $3

 

$2  $5        $4        $2        $1

 

$9  $6        $2        $4        $5

 

  1. Write the following problem in standard form :

 

Maximize

Subject to

 

 

 

unrestricted

and also form the initial simplex table (No need to solve the problem)

 

 

  1. Obtain the minimal spanning tree corresponding to the following network

 

 

3

 

 

1

6

4

9

 

5

 

 

10

 

7             5          8

 

 

3

 

 

 

  1. Draw the time schedule for the following network and identify red flagged activities

 

 

 

 

25
5

 

B                                                             F

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

  1. Express a transportation problem as Linear programming problem.

 

SECTION C    (2x 20=40)

Answer any TWO of the following. Each carries TWENTY marks.

 

  1. Solve the following problem using big-M method

Maximize

subject to

 

 

 

  1. Solve the following network problem using Floyd’s algorithm

 

 

 

5

 

3

 

 

 

6                      4

 

10

 

15

 

 

  1. Solve the following 2 x 4 game graphically

 

 

B1       B2       B3       B4

 

A1       2          2          3          -1

 

A2       4          3          2          6

 

 

  1. Find the critical path corresponding to the following project network and draw the time schedule

 

 

 

`               A  5                                         J 7                           K 3

C 8

 

 

B 10                       F 10                                        L 8

D 9                   E 4

 

 

I 1                                                  H 5                       M 4

G 3

 

 

 

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Loyola College B.Sc. Statistics April 2006 Numerical Methods Using C Question Paper PDF Download

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             LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

AC 11

FOURTH SEMESTER – APRIL 2006

                                              ST 4202 – NUMERICAL METHODS USING C

(Also equivalent to STA 202)

 

 

Date & Time : 29-04-2006/9.00-12.00         Dept. No.                                                       Max. : 100 Marks

SECTION A

Answer ALL questions                                                                              [10×2 =20]

  1. Distinguish between a compiler and an interpreter
  2. Explain the importance of #define directive
  3. Define a] a variable b] a constant
  4. What is initialization? Why it is important?
  5. Mention any four C’s fundamental data types?
  6. Write the importance of bitwise operators
  7. What is an array? Define an array to store six subjects marks for 100 students.
  8. Distinguish between an array and a structure.
  9. What are different categories of functions?
  10. Define Interpolation .

SECTION B

 Answer any FIVE questions                                                                          [5×8 =40]

  1. Write a program to find the mean and standard deviation of n numbers.
  2. Using Newton-Raphson’s method , write a C program to evaluate a real root for the  equation:
    X3 + 2 X2 + 2 X +5 =0.
  3. Write a program to the maximum of N numbers
  4. Distinguish between do and while statements with an example.
  5. Write a C program for Lagrange’s interpolation formula.
  6. Explain the following operators in C with suitable examples
    a)arithmetic operators b) increment and decrement operators
  7. Write a C program to arrange n numbers of an array in the ascending order.
  8. Write a program that uses an user defined function namely Mystrlen() which counts and returns the length of a string .

SECTION C

Answer any TWO questions                                                                         [2 x 20 =40]

  1. Write a program to read the values of matrices viz. Am x l and Bl x n  and compute the product of the matrices and store the results in the matrix Cmxn.
  2. a] Write a program in C to find the roots of a quadratic equation.

b]   Using Trapezoidal rule, Write a program to evaluate the integral                           [12]

21         Write a C program to solve the system of linear equations by GAUSS’s elimination    method.

  1. a] Write a program that prints first n-fibonacci numbers in the series.

b]   Using Newton’s backward formula, find the annual premium at the age of 33 from the            following data:  Age in years              : 24           28          32           36           40

Annual premium in Rs.             : 28.06     30.19      32.75      34.94      40

 

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Loyola College B.Sc. Statistics April 2006 General Economics Question Paper PDF Download

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             LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc./B.COM. DEGREE EXAMINATION – STATISTICS /COMMERCE

RF 7

SECOND SEMESTER – APRIL 2006

                                                       EC 2103 – GENERAL ECONOMICS

(Also equivalent to EC 3103/ECO 103)

 

 

Date & Time : 27-04-2006/1.00-4.00 P.M.   Dept. No.                                                       Max. : 100 Marks

PART – A

Answer any FIVE questions in about 75 words each.       (5 ´ 4 = 20 Marks)

  1. Distinguish between cardinal utility analysis and ordinal utility analysis?
  2. What do you understand by Oligopoly?
  3. What is meant by effective demand?
  4. Write short notes on Average Propensity to Consume and Marginal Propensity to Consume.
  5. What are the components of high-powered money?
  6. Distinguish between fees and license fees.
  7. Define Budget.

PART – B

Answer any FOUR questions in about 250 words each.   (4 ´ 10 = 40 Marks)

  1. Briefly explain the various concepts of national income analysis.
  2. Analyse the innovation theory of profit.
  3. Bring out the implications of Keynes psychological law of consumption.
  4. Distinguish between (a) Capital and investment (b) Financial investment and Real investment (c) Autonomous investment and Induced investment.
  5. Explain the determinants of money supply.
  6. Elaborate the various credit control methods.
  7. Elucidate the various types of budget. What are the qualities of a good budget?

PART – C

Answer any TWO questions in about 900 words each.     (2 ´ 20 = 40 Marks)

  1. State and explain the price-output determination under perfect competition
  2. Briefly explain the law of variable proportion.
  3. Explain the various factors influencing consumption expenditure.
  4. Trace the evolution of money and also explain the functions of money.

 

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Loyola College B.Sc. Statistics April 2006 Distribution Theory Question Paper PDF Download

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             LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

AC 15

FOURTH SEMESTER – APRIL 2006

                                                      ST 4501 – DISTRIBUTION THEORY

(Also equivalent to STA 503)

 

 

Date & Time : 27-04-2006/9.00-12.00         Dept. No.                                                       Max. : 100 Marks

 

 

SECTION A

Answer ALL the Questions                                                            (10 ´ 2 = 20 Marks)

 

  1. Define Binomial distribution.
  2. Find the p.g.f. of Poisson distribution.
  3. Give any two applications of Geometric distribution.
  4. Write down the probability density function (p.d.f.) of Gamma distribution.
  5. State the mean of Beta distribution of II kind and the condition for it to exist.
  6. If X ~ N( 0, 1),  what is the value of E(X4)?
  7. Write down the Mean deviation about median of a normal distribution.
  8. State the relation between c2 and F distributions.
  9. State the conditions under which Binomial distribution tends to a normal distribution.
  10. Define order statistics and give an example.

 

SECTION B

Answer any FIVE Questions                                                            (5 ´ 8 = 40 Marks)

 

  1. Let X have the distribution with p.m.f.

X :   -1        0       1

Pr:   0.3      0.4     0.3

Find the distributions of (i) X2   (ii) 2X +3

  1. Find the mode of Binomial distribution.
  2. Derive the conditional distributions associated with a Trinomial distribution.
  3. Derive the mean and variance of Uniform distribution on (a,b).
  4. For N(m,s2) distribution, show that the even order central moments are given by m2n = 1.3…..(2n – 1) s2n ” n ³ 1.
  5. Show that the limiting form of Gamma distribution G(1, p ) as p ®µ, is normal distribution.
  6. Define Student’s t in terms of Normal and Chi-Squared variates and derive its p.d.f.

 

  1. Let

e– ( x – q ), x > q

f(x ; q) =

0, otherwise,

where q Î R. Suppose X1,X2,…,Xn denote a random sample of size n from the

above distribution find E(X(1)).

 

 

SECTION C

Answer any TWO Questions                                                          (2 ´ 20 = 40 Marks)

 

  1. (a)Let f(x, y) = 2, 0 < x < y < 1 be the joint p.d.f of (X,Y). Find the marginal and conditional distributions. Examine whether X and Y are independent.

(b) Derive the m.g.f of Trinomial distribution.                                     (12 + 8)

  1. (a) Show that for a normal distribution Mean = Median = Mode.

(b) Show that, under certain conditions (to be stated), the limiting form of

Poisson distribution is Normal distribution.                                         (15 +5)

 

  1. (a) Let the joint p.d.f of (X1, X2) be

f(, ) = exp(–),  , > 0

Obtain the joint p.d.f. of Y1 = X1 + X2 and Y2 = X1 / (X1 + X2).

(b)Show that mean does not exist for Cauchy distribution.                   (12 +8)

 

  1. (a) Find the joint density function of i th and j th order statistics.

(b) Let X1,X2,…,Xn be  a random sample of size n from a standard uniform

distribution. Find the covariance between X (1) and X (2).                      (6 + 14)

 

 

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Loyola College B.Sc. Statistics April 2006 Design & Analysis Of Experiments Question Paper PDF Download

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             LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

SIXTH SEMESTER – APRIL 2006

                                       ST 6600 – DESIGN & ANALYSIS OF EXPERIMENTS

(Also equivalent to STA 600)

 

 

Date & Time : 19-04-2006/FORENOON     Dept. No.                                                       Max. : 100 Marks

 

 

Part – A

Answer all the questions.                                                                      10 ´ 2 = 20

 

  1. Define mixed effect model.
  2. Define orthogonal contrast.
  3. What is an experimental unit?
  4. Define uniformity trial.
  5. What do you mean by randomized block design?
  6. Write any two advantages of completely randomized design.
  7. Under what conditions can LSD be used?
  8. When a BIBD is called symmetric?
  9. Define resolvable design.
  10. What is the need for factorial experiments?

Part – B

 

Answer any five questions.                                                                     5 ´ 8 = 40

 

  1. Explain the basic principles in the design of experiments.
  2. Compute the least square estimates of randomized block design
  3. A randomized block experiment has been carried out in 4 blocks with 5 treatments A, B, C, D and E. The reading for treatment B in block 2 is missing. Explain the procedure of obtaing the estimate of one missing observation in the above design.
  4. Complete the following table for the analysis of variance and give your conclusion.
Source of variance Sum of square D. F M.S.S Variance Ratio
R

C

T

Error

 46.67

—–

—–

—–

 4

—–

—–

—–

 —–

—–

49.152

2.336

 —–

1.500

—–
Total —– —–

 

  1. How do you compute effects of totals using Yate’s method for 32?
  2. Derive main effects and interaction effects for 22 factorial experiments.
  3. From the following table, find out the confounded treatment combinations
 

Block

 Replication I Replication II Replication III Replication IV
1 2 3 4 5 6 7 8
abc

a

b

c

 

 ab

ac

bc

(1)

 abc

ab

c

(1)

 ac

bc

a

b

 

 abc

bc

a

(1)

 ab

ac

b

c

 

 Abc

Ac

B

(1)

 ab

bc

a

c

 

 

  1. Prove that l (v – 1) = r (k-1) for a BIBD.

 

Part – C

 

Answer any two questions.                                                                   2 ´ 20 = 40

 

  1. Explain the analysis of variance table for a one-way layout dealing with homogeneity of data relative to k groups in detail.
  2. Give the complete statistical analysis of Latin square design
  3. Analyze the following 23 completely confounded factorial design.
Block 1 Block 2
Replicate 1 ‘1’ 101 (nk)291 (np)373 (kp)391 (nkp)450 (n)106 (k)265 (p)312
Block 3 Block 4
Replicate 2 ‘1’ 106 (nk)306 (np)338 (kp)407 (nkp)449 (n)189 (k)272 (p)324
Block 5 Block 6
Replicate 3 ‘1’ 187 (nk)334 (np)324 (kp)423 (nkp)417 (n)128 (k)279 (p)323
Block 7 Block 8
Replicate 4 ‘1’ 131 (nk)272 (np)361 (kp)245 (nkp)437 (n)103 (k)302 (p)324

 

  1. a). State and prove Fisher’s inequality in BIBD.

b). Obtain the analysis of a BIBD using intra block information.            (10 +10)

 

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Loyola College B.Sc. Statistics April 2006 Computational Statistics Question Paper PDF Download

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             LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

AC 21

FIFTH SEMESTER – APRIL 2006

                                               ST 5503 – COMPUTATIONAL STATISTICS

(Also equivalent to STA 508)

 

 

Date & Time : 02-05-2006/1.00-4.00 P.M.   Dept. No.                                                       Max. : 100 Marks

 

 

Answer ALL the questions.  Each question carries 34 marks.

  1. a) Fit a straight line trend to the following data:

Year :     1976    1977    1978    1979    1980    1981    1982    1983

Sales:      76        80        130      144      138      120      174      190

(Rs.Lakhs)

Also estimate sales for the year 1990.

  1. b) Find seasonal indices using ratio to moving average method for the following data:

Quarter

Year       I          II        III        IV

1979      30        40        36        34

1980      34        52        50        44

1981      40        58        54        48

1982      57        78        68        62

1983      86        92        80        82

(or)

  1. c) For the following data:
Commodity Base year Current year
Price Quantity Price Quantity
A 10 12 15 10
B 16 14 20 12
C 12 15 14 13
D 18 18 22 16
E 20 22 25 20

Find i) Fisher’s  ii) Walsh’s       iii) Dorbish-Bowley
iv) Marshall-Edgeworth price index numbers

  1. d) Find seasonal indices using ratio-to-trend method for the following data

Quarter

Year       I          II        III        IV

1980     40.3     44.8     46.0     48.0

1981     50.1     53.1     55.3     59.5

1982     47.2     50.1     52.1     55.2

1983     55.4     59.0     61.6     65.3

  1. a) In a genetical experiment the frequencies observed in four classes are 1997, 906, 904, and 32. Theory predicts that there should be a proportion .  Find the maximum likelihood estimator of the parameter and also obtain the estimate of its variance.
  2. b) Five unbiased dice were thrown 96 times and the number of times 4, 5 or 6 was obtained as shown below:

No. of dice showing :   5          4          3          2          1           0

4, 5 or 6

Frequency                     8         18        35        24        10          1

Fit a binomial distribution and test the goodness of fit at 5% level of significance.

  1. c) Use the following sample of size 15 to test the hypothesis of randomness against the alternative hypothesis of cyclic effect.

12.4        13.8     22.2     17.9     24.6     15.7     27.3

22.7        26        14.5     22        21.8     31.9     11.5     28.3

(or)

  1. d) The following is a sequence of independent observations on the random variable x with the density function , .

The observations are 1.28          1.34     0.64     1.58     0.78     0.94     1.51     1.52     1.71     0.28     0.35   0.40.   Obtain the MLE’s of 1 and 2.

  1. e)  Two horses A and B were tested according to the time (in seconds) to run a particular track with the following results:

Horse A:             28        30        32        33        33        29        34

Horse B:             29        30        30        24        27        29

Test whether the two horses have the same running capacity.  Use 5% significance level.

  1. f) A test or rating a person’s sense of humour on the scale from 0 to 150 was given to 15 married couples.  The scores of these couples were as follows:

Husband :           56        90        38        51        85        49        55        58        68                                74        83   87        60        31        89

Wife :                 49        88        51        47        53        41        52        69        83                                89        77   62        65        44        92

Use the Wilcoxon test to test if there is a difference in the average sense of humour of husbands and wives against the two sided alternative.

  1. a) In a population with N=b, the values of Yi are 8, 3,1,11, 4 and 7 respectively. Calculate the sample mean for all simple random sample of size 2 without replacement.  Verify that the sample mean is an unbiased estimate of the population mean.  Also find the variance of the sample mean.
  2. b) The following table shows the number of person (x) and the weekly expenditure on food (y) in a simple random sample of 15 families.

Family number:  1          2          3          4          5          6          7          8

x    :    2          3          3          5          4          7          2          4

y   :     14.3     20.8     22.7     30.5     41.2     28.2     24.2     30.0

 

Family number:  9          10        11        12        13        14        15

x    :    2          5          3          6          4          4          2

y   :     24.2     44.4     13.4     19.8     29.4     27.1     22.2

Estimate the mean weekly expenditure on food per person.  Also find the standard error of the estimate.

(or)

  1. c) A simple random sample of 12 households was drawn from a population of 150 households.  The following table gives the number of persons in each household and whether they had seen a dentist or not.

Household          Number of                     Dentist seen

Number               Persons                  Yes                  No

1                         5                         2                      3

2                         6                         1                      5

3                         3                         1                      2

4                         2                         1                      1

5                         3                         3                      0

6                         3                         0                      3

7                         4                         2                      2

8                         5                         1                      4

9                         3                         1                      2

10                        4                         1                      3

11                        2                         1                      1

12                        3                         2                      1

Estimate the proportion of people who had consulted a dentist and find the standard error of the estimate.

  1. d) A population of size N=20 units is divided into 2 stratum.  A sample of size n=8 is to be drawn under proportional allocation using SRS.  Find .

Stratum 1:

Unit No.:            1          2          3          4          5          6          7          8

Value:                 10        15        13        12        8          9          6          11

Stratum 2:

Unit No.:            9          10        11        12        13        14        15        16        17        18

Value:                 15        17        13        12        20        25        21        17        19        23

Unit No.:            19        20

Value:                 17        13

 

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Loyola College B.Sc. Statistics April 2006 C And C ++ Question Paper PDF Download

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             LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

FIFTH SEMESTER – APRIL 2006

                                                                   ST 5401 – C AND C ++

(Also equivalent to STA 401)

 

 

Date & Time : 17-04-2006/AFTERNOON   Dept. No.                                                       Max. : 100 Marks

 

 

PART – A

Answer all the questions.                                                                  10 ´ 2 = 20

 

  1. List the characters involved in the character set of C.
  2. How do string constants differ from character constants?
  3. Write a C program to compute the product of two given numbers.
  4. j = 1

while ( j<=4)

{

printf( “%d”, j);

j = j + 1;

}

What is the output of this program?

  1. What is an array?
  2. Define Classes.
  3. Write any two application of C++.
  4. Find errors, if any, in the following C++ statements.

cout<<”x = “ X;

cin>>x;>>y;

  1. Distinguish between private and public section.
  2. What is a function in C++?

 

PART – B

Answer any five questions.                                                                           5 ´ 8 = 40

 

  1. What are increment and decrement operators? Explain their uses with examples.
  2. When the principal, rate of interest and period of deposit are given, write a C program to compute the simple interest and the compound interest.
  3. Write a C program to find the mean of two numbers using function“.
  4. Write a C program to count the number of boys whose weight is less than 50 kgs and height is greater than 170 cm and also print their corresponding weights and heights.
  5. Explain the following conditional statements:

a). if statement            b). nested if  c). while … do and d). do while.

  1. Define overloaded functions to display two and three values.
  2. Write a C++ program to find the largest of given n positive numbers
  3. Write a C++ program to arrange a set of n values in the ascending order

PART – C

Answer any two questions.                                                   2 ´ 20 = 40

 

  1. a). The mean and variance of a set of n values x1,x2,…,xn are given by the formulas

Mean = Sxi / n

Variance = (1/n) Sxi2 – (Sxi /n)2

Write a C program to find the mean and variance.

b). Explain switch statement and give an example.                                (12 + 8)

  1. a). Write a C program for raising a whole number to a power with help of function.(Raising the value i to power j is denoted as i j in Mathematics).

b). Explain two-dimensional array and give an example.                       (13 +7)

 

  1. a). If the annul gross income of a person exceeds Rs.20,000,  he has to pay 25% of his income tax and 7% of his gross-income as profession tax. Otherwise, he has to pay 15% of his gross-income as income tax and 5% of his gross-income as profession tax.  Write a C++ program to read in the gross-income of a person and calculate the income tax and the profession tax to be paid by him.

 

b). A bank provides an interest of 10% on deposits up to Rs.8000, 12% for deposits between Rs.8001 and Rs.12000 and 15% for deposits above Rs.12000.  Write a program to calculate one year’s interest for a given deposit amount according to the above rules.                                                          (10 +10)

  1. a). Write a  C ++ program to find out whether a given number   n   is a prime number .

b). Write a C++ program to perform addition, multiplication and division of two numbers using class concept.                                                    (6+14)

 

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Loyola College B.Sc. Statistics April 2006 Basic Sampling Theory Question Paper PDF Download

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             LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

AC 14

FOURTH SEMESTER – APRIL 2006

                                                   ST 4500 – BASIC SAMPLING THEORY

(Also equivalent to STA 504)

 

 

Date & Time : 25-04-2006/9.00-12.00         Dept. No.                                                       Max. : 100 Marks

 

 

SECTION – A

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

 

  1. Define a population and give two examples.
  2. State the difference between parameter and  statistic.
  3. If there are two unbiased estimators for a parameter, then show that there are uncountable number of unbiased estimators for that parameter.
  4. Explain Lottery method of selecting a  Simple Random Sample.
  5. In SRSWOR , find the probability of selecting a given subset consisting of ‘n’ units of the population consisting of  ‘N’ units.
  6. In PPS sampling , find the probability of selecting  ith  population unit when a

simple random without replacement sample of size ‘n’ is drawn from a population

containing ‘N’ units.

  1. Show that Hansen – Hurwitz estimator is unbiased for population total.
  2. Show that the sample mean is more efficient under SRSWOR  scheme than under SRSWR scheme.
  3. In SRSWR , obtain the variance of the sample mean based on only distinct units.
  4. Describe Balanced Systematic Sampling Scheme.

 

SECTION – B

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

 

  1. Illustrate that one can obtain more than one unbiased estimator for a parameter.
  2. In SRSWOR , derive the variance of sample mean by using probabilities of inclusion.
  3. Deduct the formulae for Ŷ,  V( Ŷ ) and  v(Ŷ ) under SRSWR using the formulae for  Ŷ , V(Ŷ) and v(Ŷ) available under PPSWR.
  4. Explain the consequences of  using an LSS scheme  when  ‘N’ is not a  multiple of  ‘n’.
  5. In  Stratified Random Sampling , derive the variance and  estimated variance of the sample mean.
  6. Derive Neyman allocation formula.  Hence what do we conclude about the size of the sample taken from any stratum?
  7. Explain Circular  Systematic Sampling Scheme.  List all possible samples under this scheme when N = 7 and n = 3.
  8. In PPSWR , derive the variance of Hansen – Hurwitz  estimator for population total.

SECTION – C

 

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

 

19(a).  In SRSWOR , show that sample mean is unbiased  for population mean by

using  the probability of selecting a subset of the population as a sample.  (8)

19 (b). Describe Lahiri’s  method  and prove that this method  of selection is a

PPS  selection.  (12)

 

20(a). A population contains  5 units and it is known that

( (Y1 /P1) –  Y)2 P1 +  …  + ( (Y5 / P5) – Y)2P5  =  100.

Compare  Ŷ1  =  ((y1 /P1) + ( y2 / P2 )) / 2   and

Ŷ2  = (2/3) (y1 /P1) + (1/3) ( y2 / P2).

Find the values of  α for which

Ŷα  =  α (y1/ P1)  +  (1 – α ) (y2 / P2)  is  less efficient than Ŷ1 .(12)

20(b).  Verify whether or not the sample mean coincides with the population

mean in Centered Systematic Sampling scheme when the population is

linear. ie Yi  =   α + βi  ,   i = 1,2,…,N.   (8)

 

  1. In a population consisting of linear trend, show that a systematic sample is

less precise than a stratified random sample, with a strata of size 2 k and

2 units chosen per stratum, if n > (4k + 2)/ (k  + 1), when the 1st    stratum

contains the 1st   set of  2k units,  the 2nd stratum contains the 2nd set of 2k units

in   the population and so on.  (20)

 

  1. With 2 strata , a sampler would like to have n1  =   n2  for administrative

convenience instead of using the values given by the Neyman Allocation.

If V and Vopt  denote the variances given by n1  =  n2    and the Neyman

Allocation respectively, show that (V-Vopt )/Vopt  = ( (r-1) / ( r+1)) 2 , where

r = n1 / n2  as given by Neyman allocation.   Assume that N1  and N2  are large.

(20)

 

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Loyola College B.Sc. Statistics April 2006 Applied Statistics Question Paper PDF Download

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             LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

 

FIFTH SEMESTER – APRIL 2006

                                                        ST 5502 – APPLIED STATISTICS

(Also equivalent to STA 507)

 

 

Date & Time : 25-04-2006/1.00-4.00 P.M.   Dept. No.                                                       Max. : 100 Marks

 

 

PART – A

 

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

 

  1. Define Time series and give an example.
  2. Distinguish between a Linear Trend and a Non-Linear Trend in a Time series.
  3. Explain multiplicative model for the decomposition of a time series.
  4. What are the merits and limitations of the method of Semi-Averages?
  5. Write the steps in the construction of Chain Indices.
  6. State the four test criteria for choosing a good Index Number.
  7. Explain cost of Living Index Number.
  8. Under what situations Base Shifting of Index Numbers is necessary?
  9. What are Rates and Ratios of Vital Events?
  10. How will you determine the population at any time “t” after the census or between two censuses using births, deaths and migration statistics?

 

 

PART – B

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

 

  1. Show that for the following series of fixed base index numbers, the chain indices are same as fixed base index numbers.

 

Year :          1972   1973  1974  1975  1976  1977  1978  1979  1980  1981  1982

Index No.:    100    120    122    116    120    120    137    136    149    136    137

 

  1. From the following data on clothing prices, show that the arithmetic mean of relatives (unweighted) does not meet the time reversal test :

 

Price (in Rs.)

Item

 

  • 1983

 

A                       5.00               6.00

B                      1.00               1.50

C                      8.00               8.00

 

 

  1. Mention the uses of cost of Living Index Number.
  2. Explain the method of fitting a straight line by the principle of least squares.

 

  1. A study of demand (di ) for the past 12 years (i = 1,2,…,12) has indicated the following :

 

d i    = 100; i = 1,2,…,5

 

=   20; i = 6

 

=  100; i = 7,8,…,12

Compute a 5-year moving average.

  1. Explain the various steps involved in the method of simple averages for measuring seasonal variations. State the merits and demerits of this method.
  2. Distinguish between a stationary population and stable population. Under what situation a stable population will become a stationary population?
  3. Write a short note on Central Statistical Organisation and a National Sample Survey Organisation.

 

PART – C

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

 

19 (a). Explain the various problems that are involved in the construction of an

index number of prices. (14)

19 (b). Given below are two price index series. Slice them on the base 1974=100.

By what percent did the price of steel rise between 1970 and 1975? (6)

 

 

 

Year                  Old price index for Steel                 New price index for Steel

Base (1965 = 100)                             Base (1974 = 100)

 

  • 5                          –
  • 7 –
  • 2 –
  • 8 99.8
  • 1                   100.0
  • –                                                         3

 

 

 

20 (a)   Explain the method of three selected points for fitting the Logistic Curve to the            given data. (10)

 

20 (b)   The data below gives the average quartertly prices of a commodity for five years.
Calculate the seasonal variation indices by the method of link relatives. (10)

 

 

Year

1979     1980     1981    1982    1983

 

Quarter

 

 

I               30           35       31        31         34

II               26           28       29        31         38

III               22          22        28        25         26

IV              31          36        32        35         33

 

 

 

21(a).   An enquiry into the budget of the middle class families of a certain city revealed

that on an average the percentage expenses on the different groups were Food 45,

Rent 15, Clothing 12, Fuel 8, Light 8 and Miscellaneous 20. The group index

numbers for the current year as compared with a fixed base period were

respectively 410,150,343,248 and 285. Calculate the consumer price index

number  for the current year. Mr.X was getting Rs.240 in the base period and

Rs.430 in the current year. State how much he ought to have received as extra

allowance to maintain his former standard of living. (10)

 

21(b).   A price index number series was started with 192 as base. By 1976 it rose by

25%.  The link relative for 1977 was 95. In this year a new series was started.

This new series rose by 15 points in the next year. But during the following four

years the rise was not rapid. During 1982 the price level was only 5% higher

than 1980 and in 1980 these were 8% higher than 1978. Splice the two series

and calculate the index numbers for the various years by shifting the base to

  1. (10)

 

22(a).  Find the multiple linear regression equation of  X1   on X2   and  X3   from the data relating to three variables given below: (10)

 

 

 

X1        4        6        7      9      13         1

 

X2       15     12       8       6        4        3

 

 

          X3       30     24     20      14     10        4

 

 

22(b).  Explain any one method of national income estimation. (5)

 

22(c).  The simple correlation coefficients between temperature (X1 ),

corn yield (X2 )  and rainfall (X3 ) are r12  =  0.59, r13 =  0.46  and r23 =  0.77.

Calculate partial correlation coefficient   r12 . 3   and  multiple correlation

coefficient  R1 . 23 .  (5)

 

 

 

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Loyola College B.Sc. Statistics Nov 2006 Testing Of Hypothesis Question Paper PDF Download

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                        LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

AB 14

FIFTH SEMESTER – NOV 2006

ST 5501 – TESTING OF HYPOTHESIS

(Also equivalent to STA 506)

 

 

Date & Time : 27-10-2006/9.00-12.00   Dept. No.                                                       Max. : 100 Marks

 

 

PART – A

Answer ALL the questions.                                                        10 X 2=20 marks

 

  1. Define Type I and Type II errors.
  2. Give an example each for a simple and composite hypothesis.
  3. When do you say that a critical region is uniformly best?
  4. Define level of significance and power function of a test.
  5. Provide a testing problem for which no uniformly best critical region exists.
  6. When a distribution is said to belong to an exponential family?
  7. When a” Likelihood Ratio Test” is used?
  8. Define Sequential Probability Ratio Test.
  9. Write any two applications of chi-square distribution in testing.
  10. Write a short note on “Sign Test”.

 

 

PART – B

Answer any FIVE questions.                                                        5 X 8=40 marks

 

  1. Let X1, … X10 be a random sample of size 10 from a normal distribution      N (0, 2 ). Find  a best critical region of size  = 0.05 for testing Ho : 2 = 1  against H1: 2 = 2.
  2. Let X1, X2,…. Xn be a random sample from a distribution with the p.d.f.                         f(x;q) = q xq-1   0 < x <  zero elsewhere, where .  Find a sufficient statistic  for q and show that a UMPT of Ho : q = 6 against H1 : q < 6 is based on this statistic.
  3. Let X1,X2, …, Xn be a random sample from the normal distribution N(q,1). Show that the likelihood ratio principle for testing Ho : q = q¢, where q¢ specified, against H1 : q q¢ leads to the inequality
  4. Let X have a Poisson distribution with mean q. Find the sequential probability ratio test for testing Ho : q = 0.02 against H1 : q = 0.07.  Show that this test can be based upon the statistics   If  a0 = 0.20 and =0.10,  find co (n) and    c1 (n).
  5. Let X1,X2,… Xn denote a random sample from a distribution that is N (q,1). where the mean q is unknown. Show that there is no uniformly most powerful test of the simple hypothesis Ho: q = q¢, Where q’ is a fixed number, against the alternative composite hypothesis H1 : ¢.
  6. Let X1, X2, … Xn be a random sample from a Bernoulli distribution with parameter p, where 0<p< 1. Show that the distribution has a  monotone likelihood  ratio in the statistic Y = .

 

 

 

 

 

 

 

  1. The demand for a particular spare part in a factory was found to vary from day-to-day.  In a sample study the following information was obtained.
Day Mon Tue Wed Thu Fri Sat
No of parts demanded 1124 1125 1110 1120 1126 1115

 

Using chi-square test, test the hypothesis that the number of parts demanded does not depend on the day of  the week. Use 1% significance level.

 

  1. The lengths in centimeters of n = 9 fish of a particular species captured off the

New England coast were 32.5, 27.6, 29.3, 30.1, 15.5, 21.7, 22.8, 21.2, 19.0.

Use Wilcoxon test to test Ho : m = 3.7 against the alternative hypothesis

H1 : m > 3.7 at 5% significance level.

 

PART – C

Answer any TWO questions.                                                     2 X 20 =40 marks

 

  1. (a) State and prove Neyman –Pearson theorem.
    • Consider a distribution having a p.d.f. of the form f (x ; q)  = qx (1-q)1-x, x = 0, 1

= 0, otherwise.

Let Ho : q = and  H1: q >. Use the central limit theorem to determine the sample size n of a random sample so that a uniformly most powerful test of H0  against H1 has a power function K(q), with approximately K = 0.05 and K = 0.90.                  (10+10)

  1. Let the independent random variables X and Y have distributions that are N(q1,q3) and N (q2, q3) respectively,  where the means q1, q2 and common variance q3 are unknown.  If X 1, X2, ….,Xn and Y1, Y2, … Ym are independent random samples from these distributions, derive a likelihood ratio test for testing H0 : q1=q2 ,  unspecified and q3 unspecified against all alternatives.
  2. (a) Let X be N (0,q) and let q’ = 4, q” = 9. a0 = 0.05 and =0.10. Show that

the sequential probability ratio test can be based on the statistic

Determine  c0 (n) and c1 (n).

 

 

 

 

(b)  A cigarette manufacturing firm claims that its brand A of the cigarettes

outsells its brand B by 8%. If it is found that 42 out of a sample of 200

smokers  prefer brand A and 18 out of another random sample of 100

smokers prefer brand B  test whether the 8% difference is a valid claim.  Use

5% level of significance.                                                                     (10 + 10)

  1. (a) Below is given the distribution of hair colours for either sex in a University.

Hair colour

Fair Red Medium Dark Jet black
Sex Boys 592 119 849 504 36
Girls 544 97 677 451 14

Test the homogeneity of hair colour for either sex.  Use 5% significance level.

  • Using run test, test for randomness for the following data :

15  77  01  65  69  58  40  81  16  16  20  00  84  22  28  26  46  66  36  86  66  17  43  49  85  40  51  40  10 .                                                                                                    (10+10)

 

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Loyola College B.Sc. Statistics Nov 2006 Statistical Methods Question Paper PDF Download

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                          LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

AB 01

FIRST SEMESTER – NOV 2006

ST 1500 – STATISTICAL METHODS

(Also equivalent to STA 500)

 

 

Date & Time : 01-11-2006/1.00-4.00   Dept. No.                                                       Max. : 100 Marks

SECTION A

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

 

  1. Define Statistics.
  2. Distinguish between primary and secondary data.
  3. What are the advantages of diagrammatic and graphic presentation of data?
  4. What are the desirable properties of a good average?
  5. What purpose does a measure of dispersion serve?
  6. Interpret r when r = 1, -1, 0, where r is the correlation coefficient.
  7. What is the purpose of regression analysis?
  8. Define kurtosis.
  9. How would you distinguish between association and correlation?
  10. Check for consistency: (A) = 100, (B) = 150, (AB) = 60, N = 500.

 

SECTION B

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

 

  1. Explain the various methods that are used in the collection of primary data, pointing out their merits and demerits.

 

  1. Represent the above frequency distribution by means of a histogram and superimpose the corresponding frequency polygon. Experience (in months).

 

Experience 0-2 2-4 4-6 6-8 8-10 10-12 12-14 14-16
No. of Workers 5 6 15 10 5 4 2 2

 

  1. (i) Calculate the Geometric Mean for the following values:

85, 70, 15, 75, 500, 8, 45, 250, 40, 36.

 

(ii) An aero plane covers four sides of a square at speeds of 10000, 2000, 3000 and 4000 Kms. per hour respectively. What is the average speed of the plane in the flight around the square?

 

  1. Calculate Quartile deviation and coefficient of Quartile deviation from the following data:
Wages (in Rs.) Less than 35 35-37 38-40 41-43 Over 43
No. of wage earners 14 62 99 18 7

 

 

 

 

  1. Find Bowley’s coefficient of skewness for the following frequency distribution.
X 0 1 2 3 4 5 6
Frequency 7 10 16 25 18 11 8

 

 

 

 

  1. Fit a straight line to the following data.

 

X 6 2 10 4 8
Y 9 11 5 8 7

 

  1. The ranking of two students in two subjects A and B are as follows:

 

A 6 5 3 10 2 4 9 7 8 1
B 3 8 4 9 1 6 10 7 5 2

Calculate rank correlation coefficient.

 

  1. 300 people of German and French nationalities were interviewed for finding their preference

of music of their language. The following facts were gathered out of 100 German nationals,

60 liked music of their own language, whereas 70 French nationals out of 200 liked German

music. Out of 100 French nationals, 55 liked music of their own language and 35 German

nationals out of 200 Germans liked French music.  Using coefficient of association, state

whether Germans prefer their own music in comparison with Frenchmen.

 

SECTION C

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

 

  1. (i) Define sampling and explain the different methods of sampling.

(ii) Draw an ogive for the following distribution and calculate the median wage.

Wages 1000-1100 1100-1200 1200-1300 1300-1400 1400-1500 1500-1600
Workers 6 10 22 16 14 12

 

 

 

 

 

  1. (i) Following are the records of two players regarding their performance in cricket matches.

Which player has scored more on an average? Which player is more consistent ?

 

Player A 48 52 55 60 65 45 63 70
Player B 33 35 80 70 100 15 41 25

 

(ii) You are given the following data about height of boys and girls in a certain college. You are required to find out the combined mean and standard deviation of heights of boys and girls taken together.

 

Number Average height Variance
Boys 72 68” 9”
Girls 38 91” 4”

 

  1.  (i) Find the coefficient of correlation with the help of Karl Pearson’s method.
10 20 30 40 50
5 2 4 1 4 1
10 8 2 5 1 –
15 – 3 2 1 –
20 – 1 3 2 4
25 – – 4 2 –

 

Marks in Mathematics

 

 

Marks in

Statistics

 

 

 

 

(ii) In a group of 800 students, the number of married is 320. But of 240 students who failed, 96 belonged to the married group. Find out whether the attributes marriage and failure are independent.

 

  1. The following table gives the aptitude test scores (X) and productivity indices (Y) of 10 workers selected at random:
X 60 62 65 70 72 48 53 73 65 82
Y 68 60 62 80 85 40 52 62 60 81

 

 

 

 

  • Find the two regression equations.
  • Estimate the productivity index of a worker whose test score is 92.
  • Estimate the test score of a worker whose productivity index is 75.
  • Using the two regression equations find the correlation coefficient.

 

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Loyola College B.Sc. Statistics Nov 2006 Statistical Mathematics – II Question Paper PDF Download

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                        LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

AB 08

THIRD SEMESTER – NOV 2006

ST 3500 – STATISTICAL MATHEMATICS – II

(Also equivalent to STA 502)

 

 

Date & Time : 02-11-2006/9.00-12.00     Dept. No.                                                   Max. : 100 Marks

 

 

 

SECTION A

Answer ALL questions. Each carries 2  marks                                 [10×2=20]

 

  1. Define Hermitian matrix and give an example of 3×3 Hermitian matrix
  2. Write the formula for finding the determinant by using partioning of matrices
  3. Define Riemann integral
  4. Evaluate
  5. Define repeated limits and give an example
  6. Define improper integral of Ist   kind
  7. What are the order and degree of the differential equation ?
  8. Define continuity of functions of two variables
  9. Evaluate
  10. If X, Y are random variables with joint distribution  function F(x,y), express          Pr[k1< X ≤ k2 ,   m1 < Y ≤ m2] in terms of

 

 

SECTION B

Answer any FIVE questions                                                                    (5×8 =40)

 

  1. State and prove the first fundamental theorem of integral calculus
  2. Find the inverse of the matrix A =by using 2×2 partitioning
  3. Discuss the convergence of following improper integrals:

[a]     [b]

  1. Define Gamma distribution and hence derive its mean and variance
  2. Solve the differential eqation

 

 

 

 

  1. Investigate the existence of the repeated limits and double limit at the origin of the

function  f(x,y) =

  1. Investigate for extreme values of f(x,y) = (y-x)4 + (x-2)2, x, y Î R.

 

18 . Define Beta distribution of 2nd  kind.  Find its mean and variance by stating the

conditions for their existence.

SECTION C

Answer any TWO questions                                                             (2 x 20 =40)        

  1. [a] Find the rank of the matrix A=

[b] Find the characteristic roots of the following matrix. Also find the inverse of A

using  Cayley-Hamilton theorem, where

A=

  1. [a] Test if    converges absolutely

[b] Compute mean, mode and variance for the following p.d.f

 

  1. a] Find maximum or minimum of f(x,y) = (x-y)2 + 2x – 4xy, x, y Î

b] Show that the mixed derivatives of the following function at the origin are

different:

22.a] Let f(x,y) =    be  the joint p.d.f of (x,y).

Find the co-efficient of correlation between X and Y.

[b]  Change the order of integration and evaluate

 

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Loyola College B.Sc. Statistics Nov 2006 Probability And Random Variables Question Paper PDF Download

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                        LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

AB 02

FIRST SEMESTER – NOV 2006

ST 1501 – PROBABILITY AND RANDOM VARIABLES

 

 

Date & Time : 03-11-2006/1.00-4.00     Dept. No.                                                       Max. : 100 Marks

 

 

SECTION – A

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

 

  1. Define Mutually Exclusive Events and give an example.
  2. Using the Axioms of Probability, prove that if AB, P(A) ≤ P(B).
  3. Draw Venn Diagram to represent the occurrence of at least two of three events A, B, C.
  4. State the number of ways in which a set of 10 objects can be partitioned into three subsets of sizes 5, 3 and 2 respectively.
  5. Explain the ‘Matching Problem’ and find the probability that a specified match occurs.
  6. In an experiment of forming three-letter English words with three distinct letters, what is the probability that the first and third letters are consonants while the second one is a vowel?
  7. Four statisticians arrange to meet at Hotel Five Star in a city. But there are four hotels in the city with the same name. If each one randomly chooses a hotel, what is the probability that they will all choose different hotels?
  8. In tossing a coin thrice, what is the conditional probability that the first toss results in Head given that there are two Heads?
  9. If A and B are independent events, show that A and Bc are independent.
  10. Define a Continuous random variable.
SECTION – B

 

 

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

 

  1. State the Binomial Theorem. Using Pascal’s Triangle write down the expansion of (a + b)6.

 

  1. A study of 1000 people revealed that 500 were successful in their careers, 300 had studied Statistics and 200 had both studied Statistics and were successful in their careers. Find the probability that a randomly chosen person from the lot
  • neither studied Statistics nor is successful in his career.
  • is successful in his career but had not studied Statistics.
  • had studied Statistics but is not successful in his career.

 

  1. Two fair dice are thrown. Find the probability that (a) at least one of the dice shows up an odd number; (b) the sum of the two numbers exceeds 7.           (4 + 4)

 

  1. In a random rearrangement of the letters of the word COMMERCE, find the probability that
  • All the vowels come together
  • All the vowels occupy odd number positions. (4 + 4 )

 

  1. Show that P(A | B ) + P (Ac | B) = 1.  Give an example to show that in general  P(A | B) + P(A | Bc) ≠ 1.

 

  1. An urn contains 12 balls out of which 8 are white. A sample of size 4 is drawn one by one. Find the conditional probability that the first ball drawn is white given that the sample contained two white balls. Solve this under with replacement and without replacement selections.

 

 

 

 

 

  1. A number is drawn at random from 1 to 4. Discuss the independence of the following three events:

A: Number is < 3,  B: Number is odd,  C: Number is 1 or 4

 

  1. State and prove the ‘Multiplication Theorem of Probability’ for many events.

 

SECTION – C

 

 

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

 

  1. (a) State the Addition Theorem of Probability for two events. Hence state and prove the same for three events.

(b) Let A and B be events. For k = 0, 1, 2, express the following probabilities in

terms of P(A), P(B) and P(AB):

  • P( exactly ‘k’ of the events A and B occur)
  • P(at least ‘k’ of the events A and B occur) (8 +12)

 

  1. An urn contains 5 white and 4 black balls from which 3 balls are drawn. Find the probability that (i) all three are black, (ii) at least two are white. Solve this under with replacement, without replacement and subset (unordered) selection schemes.

 

  1. (a) State and prove the ‘Law of Total Probability’. Hence establish Baye’s Theorem.

(b) Three persons A1, A2, A3 compete for the position of finance Managers of a company. The probability for A1 to get appointed is 3/8, for A2 it is 1/2 and for A3 it is 1/8. If A1 becomes the manager, the probability that he will introduce a Bonus scheme is 3/10. The corresponding probabilities in the case of A2 and A3 are 1/3 and 3/5. Given that the Bonus scheme has been introduced, what is the probability that A1 was appointed?                                                                                 (10 +10)

 

  1. (a) A random variable X has the following p.m.f.:
x -2 -1 0 1 2
P(X =x) 1/10 1/5 2/5 1/5 1/10

 

 

 

Find the c.d.f. of X. Also. Find the mean and variance of X.

(b) If f(x) = cx2, – 1< x < 2 , is the p.d.f. of a continuous random variable X, find

the value of ‘c’ and evaluate P( 0 < X < 1).                                                (13 +7)

 

 

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Loyola College B.Sc. Statistics Nov 2006 Mathematical Economics Question Paper PDF Download

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             LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034  B.Sc. DEGREE EXAMINATION – STATISTICS

AB 11

FIFTH SEMESTER – NOV 2006

         ST 5402 – MATHEMATICAL ECONOMICS

 

 

Date & Time : 03-11-2006/9.00-12.00         Dept. No.                                                       Max. : 100 Marks

 

 

SECTION–A                  (10 X 2 = 20 Marks)

Answer all the Questions:

 

  1. ‘Supply creates its own demand’-Give your comments.
  2. Define the term : Excess Demand.
  3. Briefly explain the term Supply schedule with an example.
  4. Verify whether the following function f (x,y) = 3 x 2y + 7x y 2 + 10xy is a homogenous function or not.
  5. What are the applications of Integral calculus in Economics?
  6. The MC function is 2q2 – 16q + 11. Find TC when q = 20.
  7. Q = 30 – p , TC = 7 + 6Q + 0.5 Q2. Find Q at which the profit is Maximum.
  8. What is meant by Imperfect competition ?
  9. Given that p=a-bx is a demand function , find the maximum total revenue.
  10. Briefly explain the equilibrium point with an example.

 

SECTION-B                  (5 X 8 = 40 Marks)

 

Answer any five Questions:

 

 

  1. Calculate elasticity of Supply at p=2 from the following data :

price:                    1     2          4          6          8

quantity:            20         70        150        180        200

 

  1. Show that M.R. =A.R.[1-1/hd], wherehd is the elasticity of demand.

 

  1. State and prove Euler’s theorem for Production functions.

 

  1. If the supply law is x=a Öp-b +c where  a, b and c are constants , show that the

supply curve  is an upward sloping one and it is concave from the price axis .Find

the elasticity of supply .

 

15.Distinguish between Static models and Dynamic Models with suitable examples.

 

  1. The Demand function is q = 3000 – p, FC = 150,000 and VC =  0.2 q per Unit.

Calculate Maximum Profit.

 

  1. Establish the following:
  2. i) If AC is decreasing then MC<AC
  3. ii) If AC is increasing then M.C> A.C

iii) If AC is minimum  then M.C = A.C

 

18.Distinguish between Consumer’s Surplus and Producer’s surplus with illustration.

 

 

SECTION-C                 (2 X 20= 40 Marks)

 

Answer any Two Questions:

 

  1. a. Describe the scope and limitations of the Mathematical analysis in economics

with suitable examples.

 

  1. b. Discuss in detail about the substitution effect and income effect .

 

  1. a. Explain the significance of Euler’s theorem in production function with

suitable example.

20.b. The firm has the following total cost and demand functions

TC = 1/3 Q3 – 7Q 2 + 111Q + 50 and Q = 100- p

Find profit maximizing level of output: also find profit at this level of output.

 

  1. a. Distinguish between Utility analysis and production analysis.

 

  1. b. Derive the conditions for profit maximization.

 

  1. Write short notes on the following:
  2. Indifference Map
  3. Duopoly
  4. c) COBB-DOUGLAS production function.
  5. Excess Supply.

 

 

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Loyola College B.Sc. Statistics Nov 2006 Estimation Theory Question Paper PDF Download

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            LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034                    B.Sc. DEGREE EXAMINATION – STATISTICS

AB 13

FIFTH SEMESTER – NOV 2006

ST 5500 – ESTIMATION THEORY

(Also equivalent to STA 505)

 

 

Date & Time : 25-10-2006/9.00-12.00         Dept. No.                                                       Max. : 100 Marks

 

 

 

Part A

Answer all the questions.                                                                        10 X 2 = 20

 

 

  1. Define bias of an estimator in estimating the parametric function.
  2. Explain efficiency of an estimator.
  3. Explain Uniformly Minimum Variance Unbiased Estimator (UMVUE).
  4. What is Cramer-Rao lower bound?
  5. Define bounded completeness.
  6. State Bhattacharyya inequality.
  7. Let X1, X2 denote a random sample of size 2 from B (1, θ), 0 < θ < 1. Show that    X1 + 3X2 is sufficient for θ.
  8. Describe sufficient statistic.
  9. Explain Bayes estimation.
  10. What is BLUE?
Part B

Answer any five questions.                                                                           5 X 8 = 40

 

  1. Let X1, X2, … , Xn denote a random sample of size n from B(1, p), 0 < p < 1. Suggest an unbiased estimator of (i)  p and  (ii).  p (1- p).
  2. If Tn asymptotically unbiased with variance approaching zero as n ® ¥ then show that Tn is consistent.
  3. State and establish Factorization Theorem in the discrete case.
  4. Show that the family of Bernoulli distributions { B(1,p), 0< p < 1} is complete.
  5. State and establish Lehmann-Scheffe theorem.
  6. Let X1, X2, … , Xn denote a random sample of size n from a distribution with p.d.f.                                  e– (x-q), x ³q, q Î Â

f(x; q) =     0      , otherwise.

 

Obtain UMVUE of q.

  1. Give an example where MLE is not unique.
  2. Explain Gauss-Markov model.

 

 

 

 

 

Part C
Answer any two questions.                                                                         2 X 20 = 40

 

  1. a). Let X1, X2, … ,.Xn  denote a random sample of size n from P(q), q >0. Suggest

an unbiased estimator of i)  q        ii) 5q + 7.

b). If Tn is consistent estimator for and g is continuous then show that g(Tn)

is consistent for g().                                                                        (10 +10)

 

  1. a). Show that UMVUE is essentially unique.

b). Obtain CRLB for estimating q in case of

1

f(x ; q) =                                   , – µ < x < µ and – µ < q < µ,

  • [1 + (x – q)2 ]

 

based on a random sample of size n.                                                            (10 +10)

  1. a). State and establish Chapman – Robbins inequality.

b). Describe the method of moments with an illustration.                            (12 + 8)

  1. a). Let X1, X2, … , Xn denote a random sample of size n from N (m, s2). Obtain

MLE of q = (m, s2).

b). Illustrate the method of moments with the help of G (a, p).                   (12 + 8)

 

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Loyola College B.Sc. Statistics Nov 2006 Database Management Systems Question Paper PDF Download

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                        LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034 B.Sc. DEGREE EXAMINATION – STATISTICS

AB 12

FIFTH SEMESTER – NOV 2006

ST 5403 – DATABASE MANAGEMENT SYSTEMS

 

 

Date & Time : 06-11-2006/9.00-12.00   Dept. No.                                                     Max. : 100 Marks

 

 

SECTION A 

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

 

  1. What is a database? Explain with an illustration.
  2. Write any four major sectors in which Database concepts applied very much.
  3. Define Data Manipulation Language.
  4. What is meant by Entity-Relationship Model? Explain by an example
  5. Define Physical Data Independence in DBMS and give an example
  6. What is cross-tabulation? Give an example
  7. What is meant by Indexing a file? State its advantages over sorting.
  8. Write the importance of  SELECT   command?
  9. Define a function and state its uses
  10. Explain drop SQL command

 

 

SECTION B

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

  1. Explain Numeric, Memo and Date type fields in database records with examples.
  2. Write a FOXPRO program to find Minimum and Maximum of N numbers
  3. Illustrate the difference between Function and a Procedure
  4. Use the tables given below to answer the following questions :

a] Write an SQL statement to find the name of the customer with customer-id 192-

83-7465

 

b] Write an SQL statement to find the balances of all accounts held by the customer

with customer-id 192-83-7465

 

 

 

 

 

  1. Explain different Levels of Abstraction

 

  1. Explain a] Project operation b] Cartesian-Product operation with example

 

  1. Explain the implementation Sum and Count aggregate functions in Select SQL statement with example

 

  1. Illustrate and explain a] Primary Key b] Foreign Key

SECTION C             

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

  1. a] Discuss in detail about any four types of DBMS

b]  Write any five major components of  a DBMS? Explain each of them in detail.

  1. Explain the following control structures in FOXPRO with examples.

a] SCAN             b]  IF ELSE IF…      d] DO CASE    e] DO WHILE

  1. a] The database file MARKS.dbf database file contains the fields ID, SUB1, SUB2, SUB3,SUB4 and SUB5 . Write a FOXPRO program which prepares a report to display the Grade as ‘FIRST’ if average is greater than 60 ,  Grade as ‘SECOND’ if average  is >50 and <=60 , Grade as ‘THIRD’ if average is >40 and <=50 and otherwise  Grade as ‘FAIL’. Also extend the code to find the topper in the class and more consistent scorer with regard to appropriate statistical measures.

[b] What is a Cursor? Explain Dynamic cursor by an illustration.

 

 

22.a] Discuss the important benefits of  stored  Procedures in SQL

 

b] Write short notes about each of the following:

 

[i] Data-Mining  c] Data Warehouse  d] OLAP

 

 

 

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Loyola College B.Sc. Statistics Nov 2006 Computational Statistics Question Paper PDF Download

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                        LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034 B.Sc. DEGREE EXAMINATION – STATISTICS

AB 16

FIFTH SEMESTER – NOV 2006

ST 5503 – COMPUTATIONAL STATISTICS

(Also equivalent to STA 508)

 

 

Date & Time : 01-11-2006/9.00-12.00   Dept. No.                                                       Max. : 100 Marks

 

 

Answer FIVE questions choosing  at least two questions from each section

SECTION A                                                  ( 5 x20 =100)

1] Consider a population of  6 units with values : 1, 2, 4, 7, 8, 9

[i] Write down all possible samples of size 3 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.

2] The table given below shows the summary of data for Paddy crop census of all the 2500

farms in a state. 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 the gain in efficiency resulting from [iv] and [v] as compared with [vi]

 

 

 

3]  Five samples were collected using systematic sampling from 4 different pools located in a

region to study the mosquito larvae  population( in ‘000/ gl) ,where the mosquito population

exhibits a fairly steady rising trend. i]  Find the average mosquito population in all four pools

and also find sample means. ii]  Compare the precision of systematic sampling , SRSWOR

and Stratified sampling.

Sample Number( mosquito nos. in ‘000/ gl)

Pool #

 1 2 3 4 5
I 3 7 8 9 12
II 4 9 16 18 20
III 8 16 17 19 24
IV 14 18 23 28 32

 

4] The following data furnishes the software earnings of India (in ‘00 crore) for the time period

1996 To 2005. Fit a second degree parabola and hence predict the expected software earnings

of India for the financial year 2006.

Year 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005
Earnings(‘00Cr) 4 8 15 30 90 50 110 150 300 500

 

 

SECTION B

 

  1. a.) From the following data construct an index for 2001 taking 2000 as base by the

average of relatives method using i.) arithmetic mean and ii.) geometric mean for

averaged relatives:

 

Commodity                 Price in 2000               Price in 2001

( Rs )                             ( Rs )

 

A                               50                                   70

B                               40                                   60

C                               80                                   90

D                             110                                  120

E                                20                                   20

 

b.) Construct the consumer price index number for 2003 on the basis of 2002  from the following data using ’ family budget method’.

 

Items Price in 2002 ( Rs ) Price in 2003 ( Rs ) Weights
Food 200 280 30
Rent 100 200 20
Clothing 150 120 20
Fuel 50 100 10
Miscellaneous 100 200 20

(14+6)

 

  1. a.)  The life time of 10 electric bulbs selected randomly from a large consignment gave

the following data :

Life time (Hours )   4.2     4.6       3.9       4.1       5.2       3.8       3.9       4.3                                             4.4     5.6

Test at 5% level the hypothesis that the average life time of bulbs is 4.

  • In a cross- breeding experiment with plants of certain species, 240 offsprings were classified into 4 classes with respect to the structure of the leaves as follows:

Class :                I                       II                     III                    IV

Frequencey:        21                    127                  40                    52

 

According to theory, the probabilities of the 4 classes should be in the ratio

1: 9: 3: 3. Are these data consistent with the theory? Use 5% level.                                                                                                                                                               (10+10)

 

  1. Two samples are drawn from two normal population. From the following data, test whether the two populations have i) Equal variance ii) Equal means at 5% level.

Sample 1         60        65        71        74        76        82        85        87

Sample 2         61        66        67        85        78        63        85        86        88        91

 

 

  1. a.)  IQ Test on two groups of boys and girls gave the following results
Mean SD Sample Size
Boys 73 15 100
Girls 78 10 50

 

Is there a significant difference in the Mean scores of boys and girls ? Test at 1% level.

 

  • Let X denote the length of a fish selected at random from the lake . The

observed length of n=10 fish , were 5.0 , 3.9 ,5.2 , 5.5 , 2.8 , 6.1, 6.4 , 2.6 , 1.7

and 4.3. Test at 5 % level the hypothesis that the median length of fish in the

lake is 3.7 .                                                                                      (6+14)

 

 

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Loyola College B.Sc. Statistics Nov 2006 C And C ++ Question Paper PDF Download

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                         LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

AB 10

FIFTH SEMESTER – NOV 2006

ST 5401 – C AND C ++

(Also equivalent to STA 401)

 

 

Date & Time : 06-11-2006/9.00-12.00   Dept. No.                                                       Max. : 100 Marks

 

 

Part A

Answer all the questions.                                                                        10 X 2 = 20

 

  1. What are the special characters in C?
  2. Distinguish between string and character constants.
  3. Explain briefly increment operator with an illustration.
  4. Explain briefly “if…else” statement with an illustration in C.
  5. What is the output of the following?

int x = 0;

for (i=1; i<=5; i++)

{

x+=i*i;

printf(“%d”,x);

}

What will be the output when the above segment is executed?

  1. What are the logical expressions in C programming?
  2. int y =0, int k;

for (i=10; i>1; i++)

{

k=i*i;

cout<<k<<endl;

}

What will be the output when the above segment is executed?

  1. Write a C++ program to display the following output using a single cout statement.

Maths = 98

Physics=79

Statistics=99

  1. Define class.
  2. Define encapsulation.

 

 

Part B

Answer any five questions.                                                               5 X 8 = 40

 

  1. Electricity charges are levied in a state according to the following schedule.

Number of Units consumed                Rate / Unit

0 – 99                                      Rs. 1.50

  • 2.50

300 – 499                                Rs. 4.00

500 & above                            Rs. 5.00

Write a C program to prepare the electricity bill, when the number of units

consumed by a customer is given.

  1. Write a C program to find out the largest number from the three given numbers using an user-defined function.
  2. Explain the following control statement in C programming with an example.

a). do while

b). for statement.

  1. Explain one-dimensional arrays and write any one program of your choice in C with help of the same.
  2. Write a program to find perimeter and area of circle with help of function.                             ( note: area=pr2 and perimeter = 2pr)
  3. Calculate mean for the following data with help of C++ program.

X: 10   20        30        40        50        60        70        80        90        100

F:  2     8          9          15        25        40        30        20        18        10

  1. In a company the health insurance premium is deducted from salary as given in the following table:

Category                    Amount deducted (in %)

Single                                      9.75

Married without children        16.25

Married with children             24.50

Write a C++ program to receive as input the salary and category of a person and

calculate his insurance premium.

  1. Write C++ program to calculate standard deviation for N values using array in Class.

 

Part C

Answer any two questions.                                                               2 X 20 = 40

 

  1. a). Explain different types of constants and their rules in C programming.

b). Write a C program to calculate mean and variance for N values with the help of arrays.                                                                                                         (10+10)

  1. a). Write a C++ program to calculate sum of two matrices of order N X N.

b). When the principal, rate of interest and period of deposit are given, write a c

program to compute the simple interest and compound interest.          (10+10)

  1. a). Explain function overloading.

b). Write C++ program to calculate area of a triangle with help of function

overloading when (i) two sides and (ii) three sides are known.               (5+15)

  1.  Write a C++ program to calculate correlation coefficient of two variable X and Y

and also display mean of X and Y using the concept of class.                (10+5+5)

 

 

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