## Loyola College B.Sc. Statistics April 2012 Testing Of Hypotheses Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034B.Sc. DEGREE EXAMINATION – STATISTICSFIFTH SEMESTER – APRIL 2012ST 5505/ST 5501 – TESTING OF HYPOTHESES
Date : 27-04-2012 Dept. No.         Max. : 100 Marks                 Time : 9:00 – 12:00
PART – A
1. Distinguish between simple and composite hypothesis.2. What is meant by testing of hypothesis? 3. Define randomized test.4. Explain the meaning of level of significance. What does 5% level of significance imply?5. Which tests of hypothesis are called two-tailed tests? Give an example for it. 6. State the Likelihood Ratio Criterion.7. Write down the steps involved in a test of significance procedure for large samples.8. Define non-randomized test.9. Which types of tests are called non-parametric tests?10. Mention any two advantages of non-parametric tests.
PART – B
Answer any FIVE questions: (5×8=40 Marks)
11. Let  be the probability that a coin will fall head in a single toss in order to test  against . The coin is tossed 5 times and  is rejected if more than 3 heads are obtained. Find the probability of Type I error and power of the test.  12. Let   be a random sample from , where   is known. Find a UMP test for testing   against .13. Derive the likelihood ratio test for the mean of a normal population  when   is known.14. Derive the likelihood ratio test for the variance of a normal population  when   is known.15. Describe likelihood ratio test procedure and state its properties. 16. What is paired t test? What are its assumptions? Explain the test procedure.17. Explain the test procedure for testing the randomness of a sample.  18. Discuss the procedure for median tests.PART – C
Answer any TWO questions:       (2×20=40 Marks)
19. (a) State and prove Neymann-Pearson Lemma.      (b) Illustrate that UMP test does not exist always.20. (a) What are the applications of chi-square distribution in testing of hypothesis.             (b) Explain the test procedure for testing equality of variances of two normal populations.      21. (a) What are the applications of t-distribution in testing of hypothesis?      (b) Explain Wald-Wolfowitz Run test for two samples.22. (a) Explain the Chi-square test of independence of attributes in contingency table.             (b) Explain the sign test for one sample.

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## Loyola College B.Sc. Statistics April 2012 Statistical Process Control Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

SIXTH SEMESTER – APRIL 2012

# ST 6605/ST 6602 – STATISTICAL PROCESS CONTROL

Date : 20-04-2012              Dept. No.                                        Max. : 100 Marks

Time : 1:00 – 4:00

PART – A

1. What is quality?
2. Write the need of Total Quality Management.
3. Write the purpose of Histogram.
4. Explain Q-Q Plot.
5. What is statistical process control?
6. Define ‘C’ chart.
7. Explain process capability analysis.
8. Explain the concept of subgroups.
9. What is Acceptance Sampling?
10. Explain consumer’s risk and producer’s risk.

PART – B

1. Describe Quality improvement in the modern business environment.
2. Explain the concept of 3-sigma limits. When do you say the process is out of control?
3. Describe the Box plot technique.
4. Describe process-capability analysis using a Histogram.
5. Explain the construction ofand R charts.
6. Write the advantages of acceptance sampling.
7. What are the basic principles of CUSUM control chart?
8. Explain the technique of single sampling plan for attributes.

PART C

1. (a) State the requirements for successful implementation of TQM.

(b) Discuss the relation between quality improvement and productivity.

1. (a) Draw the stem and leaf plot for the following data:

13,15,16,22,24,28,35,32,37,26,41,85,66,45,46,49,44,50,54,58,57,59,61,62,65,93,78,74,72,77,81,82,95,34,38,39,53,55,47,64,

(b) Explain Frequency distributions and its applications.

1. (a)Explain the construction of any two control charts for attributes.

(b) Write the applications of u chart and np chart.

1. (a) Explain the construction of CUSUM control chart.

(b) Explain double sampling plan in detail.

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## Loyola College B.Sc. Statistics April 2012 Statistical Methods Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

FIRST SEMESTER – APRIL 2012

# ST 1502/ST 1500 – STATISTICAL METHODS

Date : 28-04-2012              Dept. No.                                        Max. : 100 Marks

Time : 1:00 – 4:00

PART – A

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

1. State any two limitations of statistics.
2. What is meant by classification?
3. Define dispersion.
4. Explain Kurtosis.
5. What is curve fitting?
6. Explain the principle of least squares.
7. Define correlation with an example.
8. State any two properties of regression coefficients.
9. Explain association of attributes.
10. Define Independence of attributes.

PART – B

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

1. Explain the Scope of statistics.
2. Describe Nominal and Ordinal scaling. Also write their advantages.
3. Define skewness. Explain the various measures of skewness.
4. Calculate the mean and mode for the following frequency distribution:

Monthly Wages:   Less than 200        200-400           400-600           600-800             800-100

No. of workers:              78                    165                   93                     42                        12

1. Fit a straight line trend for the following data:

Year:   1990    1991    1992    1993    1994    1995    1996

Y:         127      101      130      132      126      142      137

1. Prove that the coefficient of correlation lies between -1 and +
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. a) Arrange the following data in a 2×2 contingency table and find the unknown class frequency,

given that the total frequency is 500:

Intelligent fathers with intelligent sons  250

Dull fathers with intelligent sons             75

Intelligent fathers with Dull sons              40

1. b) Ascertain whether there is any relationship between intelligence of fathers and sons.

(P.T.O)

PART – C

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

1. a) Explain the applications of diagrams and graphs and state their advantages.

1. b) Define Primary data. What are the sources of primary data?
2. Calculate first four moments about mean from the following data. Also calculate b1 and

b2 and comment on the nature of the distribution.

X:     0        1          2          3          4          5          6          7          8

f:      5        10        15        20        25        20        15        10        5

1. a) Fit a second degree parabola to the following data:

Year:              1982  1983    1984    1985    1986    1987    1988    1989    1990

y:     4        8          9         12        11        14        16        17        26                         (12 marks)

1. b) Calculate Karl-Pearson’s coefficient of correlation from the following data.

X:  10   12   18    24     23   27

Y:  13   18    12   25     30   10                                                                (8 marks)

1. a) Given the following data, find the two regression equations:

(8 marks)

1. b) Find the missing frequencies from each of the following two data:

(i)    (A) = 400,     (AB) = 250,    (B) = 500,      N = 1200

(ii)       (B) = 600,

Is there any inconsistency in the data given above?                                       (12 marks)

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## Loyola College B.Sc. Statistics April 2012 Statistical Mathematics – II Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

THIRD SEMESTER – APRIL 2012

# ST 3503/ST 3501/ST 3500 – STATISTICAL MATHEMATICS – II

Date : 24-04-2012              Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

PART – A

Answer ALL the questions:                                                                       [10×2 =20]

1. Define upper sum and lower sum of a function defined over the

interval [a, b].

1. Examine whether the function f(x) = 1/x2 , for x≥1, is a p.d.f. If so find
2. Define improper integral of II kind.
3. Define Gamma integral and state when it converges.
4. Let u = (3y – x) / 6 and v= x / 3. Obtain the Jacobian of transformation.
5. Examine whether f(x,y) = 2, 0 < x < y < 1, is a bivariate probability density function.
6. When do we say that a differential equation is variables separable? Show that (1 – x) dy

(3 + y) dx = 0 is variables separable.

1. Obtain the Laplace transform of g(t) = e-λt , t > 0.
2. Define characteristic equation and characteristic roots.
3. State Cayley Hamilton Theorem.

PART – B

Answer any FIVE questions:                                                                      [5×8 =40]

1. Evaluate from first principles.
2. Show that every continuous function defined on a closed interval of the real line is

Riemann integrable.

1. Obtain the moment generating function of the two parameter Gamma distribution. Hence

find the mean and variance.

1. Discuss the convergence of the integral

xm-1(1-x)n-1dx.

1. Solve the differential equation:

.

1. State and prove Initial Value and Final Value Theorems of Laplace transforms.
2. If λ is the characteristic root of a non-singular matrix A, show that is the characteristic

root of the matrix .

1. Find the characteristic roots and corresponding vectors of the matrix A where

.

PART – C

Answer any TWO questions:                                                                     [2×20 =40]

1. (a) If f(x) and g(x) are two Riemann-integrable functions, then show that the sum

f(x) + g(x) is also Riemann integrable.

(b) State and Prove the First Fundamental Theorem of integral calculus.

1. (a) Establish the relation between the Beta function and Gamma function. Hence find the

value of β(1/2, 1/2).

(b) For a non-negative function f(t) =tn  show that

.Γ(n+1).

1. (a) Solve the following differential equation using Laplace transform, where y(0) = 3 and

y ¢(0) = 6 :

.

(b) Obtain the inverse transform of

1. Verify Cayley-Hamilton Theorem for the matrix and hence, find the inverse

of A.

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## Loyola College B.Sc. Statistics April 2012 Statistical Mathematics – I Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

SECOND SEMESTER – APRIL 2012

# ST 2502/ST 2501/ST 2500 – STATISTICAL MATHEMATICS – I

Date : 16-04-2012                   Dept. No.                                          Max. : 100 Marks

Time : 9:00 – 12:00

PART – A

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

1. Define monotonically decreasing sequences.
2. Define random variable.
3. Define divergence sequences.
4. What is meant by linear dependence?
5. 5. Find the trace of the matrix A =
6. State Rolle’s Theorem.
7. The probability distribution of a random variable X is: Determine       the constant k.
8. Define symmetric matrix. Give an example.
9. Find the determinant of the matrix
10. Define stochastic matrix.

PART – B

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

1. The diameter, say X, of an electric cable, is assumed to be continuous random variable with p.d.f
2. i) Check that the above is a p.d.f. ;   ii) Obtain an expression for the c.d.f of x ;

iii)  Compute ;  iv) Determine the number K such that P(X < k) = P(X > k)

1. Prove that a convergent sequence is also bounded.
2. By using first principles, show that the sequences , where, n = 1, 2, . . . ,

converges to   .

1. Show that differentiability of a function at a point implies continuity. What can you say about the

1. State and prove Lagrange’s Mean Value Theorem. (P.T.O.)
2. Obtain the Maclaurin’s Series expansion for log(1+x), for – 1 < x < 1 .
3. If the joint distribution function of X and Y is given by
4. a) Find the marginal densities of X and of Y ;     b) Are X and Y independent?
5. c) Find P(X  1 Y ;
6. Find inverse of the matrix

PART – C

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

1. Examine the validity of the hypothesis and the conclusion of Rolle’s theorem for the          function f defined in  in each of the following cases:
2. i) , a = 0, b = 2
3. ii) , a = -3, b = 0
4. Two fair dice are thrown. Let X1 be the score on the first die and X2 the score on the second die. Let Y denote the maximum of X1 and X2 i.e. max(X1, X2).
5. a) Write down the joint distribution of Y and X1.
6. b) Find E (Y), Var (y) and Cov (Y, X1).
7. Suppose that two-dimensional continuous random variable (X, Y) has joint probability density        function given by
8.  i) Verify that
9.   ii) Find P (0 < X <,  P(X+Y < 1),  P(X > Y),  P(X < 1 | Y < 2)
10. (a) Find the rank of .

(b) Verify whether the vectors (2, 5, 3), (1, 1, 1) and (4,–2, 0) are linearly independent.       (10 +10)

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## Loyola College B.Sc. Statistics April 2012 Probability And Random Variables Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

FIRST SEMESTER – APRIL 2012

# ST 1503/ST 1501 – PROBABILITY AND RANDOM VARIABLES

Date : 02-05-2012              Dept. No.                                        Max. : 100 Marks

Time : 1:00 – 4:00

PART –A

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

1. Distinguish between Mutually Exclusive event and Independent event.
2. Prove that for any event A in S, P( A ∩ AC ) = 0.
3. Suppose from a pack of 52 cards one card is drawn at random, what is the probability that it is either a king or a queen.
4. A fair coin is tossed 5 times. What is the probability of having at least one head?
5. Prove that if P(A) > P(B), then P(A│B) > P(B│A)
6. If two events A and B are independent, show that (i) AC and BC are independent.
7. Out of 800 families with 4 children each, how many families would be expected to have at least one boy?
8. A bag contains 5 white and 3 black balls.  Two balls are drawn at random one after the other without replacement.  Find the probability that both balls drawn are black.
9. A fair coin is tossed three times.  Let X be the number of tails appearing.  Find the probability distribution of X .  Calculate E(X).
10. State addition theorem of probability for two events A and B.

PART –B

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

1. Given P(A) = 1/ 3, P(B) = 1/ 4 and P (A ∩ B ) = 1 / 6

Find the following probabilities  (i) P ( AC ) , (ii) P ( AC  ÈB ) and (iii) P ( AC ∩ BC ).

12 . (a) An MBA candidate applies for a job in two firms X and Y.  The probability of his being selected

in firm X is 0.7 and being rejected at Y is 0.5.  The probability of at least one of his

applications being rejected is 0.6.  What is the probability that he will be selected in one

of the firms?

(b) What is the chance that a leap year selected at random will contain 53 Sundays?

13 (a) A pair of dice is rolled.  If the sum of  9 has appeared, find the probability that one of the

dice shows 3.

(b) Two a’s and b’s are arranged in order.  All arrangements are equally likely. Given that the

last letter, in order is b’ find the probability that the two a’s are together.

1. Two urns contain 4 white and 6 black balls and 4 white and 8 black balls.  One urn is selected at random and a ball is taken out.  It turns out to be white.  Find the probability that it is from the first urn.
2. It is given that P( AÈB ) = 5 /6 , P ( A ∩B ) = 1 /3 and P ( BC ) = 1/ 2.  Show that the

events A and B are independent.

1. Let X be a continuous random variable with p.d.f given by

f(x) = K x         ,       0 ≤ x < 1

= K            ,       1 ≤ x < 2

= ─ Kx + 3 K  ,  2 ≤ x ≤ 3

=  Otherwise

• Determine the constant K (ii)  Determine F(x)
• State and prove Multiplication law of probability.
• In four tosses of a coin, let X be the number of heads. Tabulate the 16 possible outcomes with the corresponding values of X. By simple counting, derive the probability distribution of X and hence calculate the expected value of X.

SECTION – C

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

• a) Three groups of children contain respectively 3 girls and 1 boy and 2 girls and 2 boys and 1 girl

and 3 boys.  One child is selected at random from each group.  Find the chance that the 3

selected comprise 1 girl and 2 boys.

1. b) A, B and C go for bird hunting . A has record of 1 bird out of 2, B gets 2 out of 3 and C gets 3

out of 4.  What is the probability that they will kill a bird at which all shoot simultaneously?

• a) An unbiased coin is tossed three times. Let A be the event “ not more than one head” ,

and let B be the event “ at least one of each face “.  Are A and B independent?

1. b) Two persons A and B attempt independently to solve a puzzle. The probability that A will

solve it is 3/5 and the probability that B will solve it is 1/3.  Find the probability that the

puzzle will be solved by (i) at least one of them and (ii) both of them

1.   a) State and prove Baye’s Theorem.
2. b) If A, B, C are mutually independent events then prove that and C are also independent.
3. The length of time ( in mintues) that a certain lady speaks on the telephone is found to be

random phenomenon, with a probability function specified by the probability density

function f(x) as

f(x) = A e  – X / 5   , for x ≥ 0

=  0 otherwise.

• Find the value of A that make p.d.f
• What is the probability that the number of minutes that she will talk over the phone is (i) more than 10 minutes (ii) less than 5 minutes (iii) between 5 and 10 minutes?

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## Loyola College B.Sc. Statistics April 2012 Operations Research Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B. Ss. DEGREE EXAMINATION – STATISTICS

SIXTH SEMESTER – April 2012

ST6604 / ST6601 – OPERATIONS RESEARCH

Date: 18-04-2012                   Dept. No.                                                            Max.:100 Marks

Time: 1.00 – 4.00

PART – A

Answer ALL questions:                                                                       (10 x 2  = 20)

1. What are the different phases of Operations Research?
2. What is a degenerate solution?
3. Give the dual for the following primal:
1. When can dual simplex method be applied to a LPP?
2. Define Two- person zero sum game.
3. Mention the two phases in the two-phase method.
4. When is there a necessity for artificial variables?
5. What are the methods used to solve a mixed strategy game?
6. What is CPM?
7. What is Minimax criterion?

PART – B

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

1. Explain simplex method for solving an LPP.
2. The manager of an oil refinery must decide on the optimum mix of two possible blending processes of which the input and output production runs are as follows:
 Process Input Output Crude A Crude B Gasoline X Gasoline Y 1 6 4 6 9 2 5 6 5 5

The maximum amounts available of crudes A & B are 250 units and 200 units respectively. Market demand shows that at least 150 units of gasoline X and 130 units of gasoline Y must be produced. The profits per production run from process 1 and process 2 are Rs. 4 and Rs. 5 respectively. Formulate the problem for maximizing the profit.

1. What are the steps involved in solving an unbalanced transportation problem to get the optimum solution?

1. A departmental head has four subordinates and four tasks to be performed. The subordinates differ in efficiency and the tasks differ in their intrinsic difficulty. His estimate of the time each man would take to perform each task, is given in the matrix below:
 Tasks Men E F G H A 18 26 17 11 B 13 28 14 26 C 38 19 18 15 D 19 26 24 10

How should the tasks be allocated, one to a man, so as to minimize the total man-hours?

1. Solve the following graphically:

Player B

Player A

1. Differentiate between Simplex method and Dual Simplex method.
2. Explain Laplace and Savage criterion in detail.
3. Explain PERT algorithm in detail.

PART – C

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

1. a) Explain Primal – Dual Relationship.                                                          (5)

1. b) Use Duel Simplex method to solve the following LPP.                            (15)

Minimize z = 6x1 + 7x2 + 3x3 + 5x4

Subject to

5x1 + 6x2 – 3x3 + 4x4 ≥ 12

x2 – 5x3 –  6x≥ 10

2x1 + 5x2 + x3 +   x4   ≥  8

x1, x2, x3, x4 ≥ 0

1. a) Show that for any zero-sum two-person game where there is no saddle point and for

which A’s payoff matrix is

(15)

the optimal strategies (x1, x2) and (y1, y2) for A and B respectively are determined by

What is the value of the game?

1.             20. b) What is the principle of dominance in game theory?                                          (5)

1. Find the initial basic feasible solution for the given transportation problem using:

(i)  North West Carner rule        (ii) Vogels method          (iii) Least Cost method.

 From To Available A B C I 50 30 220 1 II 90 45 170 3 III 250 200 50 4 Requirement 4 2 2

And obtain the optimal solution.

1. a) What are the rules for constructing a network diagram?                            (5)

22.  b) A project consists of eight activities with the following relevant information:

 Activity Immediate Predecessor Estimated duration (days) Optimistic Most likely Pessimistic A – 1 1 7 B – 1 4 7 C – 2 2 8 D A 1 1 1 E B 2 5 14 F C 2 5 8 G D, E 3 6 15 H F, G 1 2 3

(i)  Draw the PERT network and find out the expected project completion time.

(ii) What duration will have 95% confidence for project completion?

(iii) If the average duration for activity F increases to 14 days, what will be its effect on the expected project completion time, which will have 95% confidence?

(15)

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## Loyola College B.Sc. Statistics April 2012 Numerical Methods Using C Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

THIRD SEMESTER – APRIL 2012

# CS 3203 – NUMERICAL METHODS USING C

Date : 02-05-2012              Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

PART – A

ANSWER ALL THE QUESTIONS:                                                                       (10 X 2 =20)

1. What is meant by identifier?
2. Give the syntax for conditional operator in C.
3. How will you declare a variable in C?
4. List out any four built in functions in C.
5. Write a transpose of a given matrix.

15   16   17

13   15   16

15   15   18

1. State the formula for Newton’s backward interpolation.
2. Differentiate the equation 5X5+2X 4+ 2X3 + 14X +45.
3. What is the use of Newton- Raphson method?
4. Give the formula for Simpson 3/8 rule.
5. What is the use of power method?

PART – B

ANSWER ALL THE QUESTIONS:                                                                         (5 X 8 =40)

1. a) Explain all types of if statements in C with suitable example.

(Or)

1. b) Write a C program to find out sum and average of n numbers.

1. a) Write a C program to find out factorial of n numbers using recursion.

(Or)

1. b) Discuss about all the operators used in C.

1. a) Solve the system of equation using Gauss Jordan method.

2x + 4y – 6z =  -8

x + 3y +  z  = 10

2x  – 4y – 2z = -12

(Or)

1. b) Write a C program to solve the system of equation using Gauss elimination

method.

1. a) Write a C program to implement Simpson’s 1/3 rule.

(or)

b). Evaluate the following integral using trapezoidal rule.

F(x) = 1/ (1+x2) with n = 10 on the interval [0-1].

1. a) Write a C program to find out root of the equation using Regula –Falsi method.

(Or)

1. b) Estimate theg given equation u’ = -2tu2 with h = 0.2 on the interval [0-1] using

Euler’s method.
PART – C

ANSWER ANY TWO QUESTIONS:                                                               (2 X 20 =40)

1. a) Explain scanf() and printf() statement in C with suitable example.
2. b) Illustrate the use of user defined function in C.
3. a) Write a C program to find out biggest of any three given numbers .
4. b) Estimate the value of y at x = 6 using Newton’s forward interpolation formula with the help of

the following table.

 x 3 7 9 10 Y 168 120 72 63

1. a) Write a C program to implement Runge –kutta IVth order method.
2. b) Compute the root of the given equation using Bisection method.

X3 – 5X + 1 = 0 with the initial value a0 =0 and b0 =0

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## Loyola College B.Sc. Statistics April 2012 Finan.A/C & Financial Statement Analysis Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

SECOND SEMESTER – APRIL 2012

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

Date : 23-04-2012              Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

Section A

Answer all the questions:                                                                              (10 X 2 = 20 marks)

1. Name any four parties who are interested in accounting information?
2. What is meant by contra entries? Give example.
3. How is Legacy treated in the accounting books of a Non trading organization?
4. Name any four accounting concepts.
5. Plant and machinery is …………asset (fixed/current)
6. Motor vehicles account is a …………. (Personal/ Real/ Nominal) account
7. Ascertain the gross profit ratio:

Cost of goods sold . 70,800 ;            Sales . 1,30,200

1. From the following information compute the tax paid during the year:

Provision for tax(1-4-2011)    . 30,000

Provision for tax(31-3-2012)  .45,000

Tax provided during the year . 30,000

1. Calculate the amount of salaries to be shown in Receipts and Payments Account:

.

Salaries as per Income and Expenditure Account                  1,500

Paid in advance in previous year                                               700

Outstanding at the end of current year                                      300

Outstanding at the end of previous year                                   800

1. Calculate the profit or loss on sale of machinery:

Original cost . 1,00,000;        Accumulated depreciation . 25,000;

Sale value . 50,000

1. Choose the correct alternative
2. Receipts and Payments Account is a summary of

i)Income and expenses account          ii) Cash receipts and Payments

iii) Debit and Credit balances of ledger accounts

1. Goods worth . 1,000 taken by the proprietor for personal use should be credited to

i)Purchases account            ii) Sales account          iii) Drawings account

Section B

Answer  any five questions                                                                     (5 X 8 = 40 marks)

1. Define Accounting. What are the objectives of Accounting?
2. What is a Bank Reconciliation Statement? What are the causes of difference between a Pass book and Cash book?
3. Differentiate between Receipts and Payments Account and Income and Expenditure Account.

1. Enter the following transactions in a Petty cash book:

2012                                                                                                       .

Jan 1    Received from main cashier as imprest cash balance              1,000

7    Bought postage stamps                                                              200

15    Paid for cartage                                                                            25

20    Paid taxi hire                                                                                75

23    Purchased stationery                                                                    35

25    Paid to travel agent for snacks                                                     15

30    Courier services                                                                            25

31    Office cleaning                                                                            20

1. Journalise the following transactions:

2012

April 1             Mr. Xavier brought cash . 1,50,000 to start a business

April 2             He deposited . 1,25,000 in a newly opened bank account

April 4             He purchased goods for cash . 8,000

April 7             He purchased goods for . 10,000 payment was made through bank

April 8             Mr. Xavier withdrew . 2,000 from the bank for office use

April 10           He withdrew . 1,000 from the bank for celebrating his son’s birthday

April 14           He paid salary in cash .250

April 18           He gave cheque to Mr. Anand, the landlord for rent . 3,000

1. Enter the following transactions into proper subsidiary books:

2012

Jan 1     Purchased goods from Paul of the list price of . 50,000 less 10% trade discount

6      Sold goods to Rahul for . 10,000

8      Ramesh sent goods for . 40,000

12     Purchased a delivery van from Mahendra . 2,00,000

18     Sold goods to James for . 12,000

20     Returned goods to Paul, of the list price of . 5,000

22     Sent goods to Amir for . 6,000

24     Sold old newspaper for . 200

27     Sold goods to Rohit for . 8,000

1. From the following particulars, prepare Income and Expenditure Account:

.

Fees collected, including . 80,000 on account of the previous year             3,80,000

Fees for the year outstanding                                                                            10,000

Salary paid, including . 3,000 on account of the previous year                       28,000

Salary outstanding at the end of the year                                                            1,000

Entertainment expenses                                                                                       3,000

Tournament expenses                                                                                         12,000

Meeting expenses                                                                                               18,000

Travelling expenses                                                                                              6,000

Purchase of books and periodicals,

including . 19,000 for purchase of books                                            29,000

Rent                                                                                                                   10,000

Postage                                                                                                                 4,000

Printing and stationery                                                                                       15,000

1. From the following particulars, determine the maximum remuneration available to a

part time director  and manager of a manufacturing company.

The Profit & loss Account of the company showed a net profit of .20,00,000 after taking into account the following items:

.

• Depreciation (including special depreciation of . 20,000) 50,000
• Donation to political parties 25,000
• Provision for income tax          1,00.000
• Ex-gratia payment to a worker   5,000
• Capital profit on sale of assets   7,500
• Preliminary expenses   5,000
• Profit on sale of investment          4,20,000
• Multiple shift allowance          2,10,000

Section C

Answer any two questions:                                                                    (2 X 20 = 40 marks)

1. The following balances were taken from the trial balance of Mr. Mohammed

as on 31-3-2012

 Particulars Particulars . Furniture(on cost) Delivery van Building(on cost) Bad debts Debtors Stock (1-4-2011) Purchases Sales return Advertisement Interest Cash Tax General expenses Salary 64,000 6,25,000 7,50,000 12,500 3,80,000 3,46,000 5,47,500 20,000 45,000 1,11,800 65,000 25,000 78,200 3,30,000 Capital Creditors Provision for Bad debts Overdraft Sales Purchase return Commission 12,50,000 2,50,000 20,000 2,85,000 15,45,000 12,500 37,500 34,00,000 34,00,000

1. Depreciate Building 5%, Furniture 10%
2. Commission received . 12,500 is related to next year

iii.  Create provision on debtors for bad debts @ 6%

1. Stock (31-3-2012) . 3,25,000

Prepare Trading & Profit & loss account and Balance sheet as on 31- 3- 2012

1. From the following balance sheets, prepare cash flow statement:
 Liabilities 2010 2011 Assets 2010 2011 Share capital General reserve Profit & loss A/c Bank loan Creditors Provision for tax 2,00,000 50,000 30,500 70,000 1,50,000 40,000 2,50,000 60,000 30,600 – 1,35,200 35,000 Building Machinery Stock Debtors Cash Goodwill 2,00,000 1,50,000 1,00,000 80,000 500 10,000 1,90,000 1,69,000 74,000 64,200 8,600 5,000 5,40,500 5,10,800 5,40,500 5,10,800

During the year:

• Dividend of . 23,000 was paid

(ii)  Machinery was purchased for . 8,000

(iii) There is no sale of building or machinery

(iii) Income tax paid during the year . 33,000

1. a Stock turnover ratio                        3 times ;           Cost of goods sold      . 2,40,000

Stock in the beginning is . 20,000 more than the stock in the end. Calculate stock in  the beginning and at the end                                                                    (4 marks)

1. From the following particulars, prepare a statement showing the proprietor’s fund as on 31st December 2011 with as many details as possible (16 marks)

Current ratio          2.5                   Fixed assets to Proprietors funds        0 .75/2

Acid test ratio       1.5                   Reserves and surplus                           . 60,000

Working capital     .90,000          Bank overdraft                                    . 15,000

Long term debt     nils

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## Loyola College B.Sc. Statistics April 2012 Estimation Theory Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

FIFTH SEMESTER – APRIL 2012

# ST 5504/ST 5500 – ESTIMATION THEORY

Date : 25-04-2012              Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

PART-A

• Define consistent estimator.
• State the characteristics of a good estimator.
• Define sufficient statistic.
• State factorization theorem.
• Mention any two properties of MLE.
• Explain the concept of method of moment estimation.
• Define prior and posterior probability distribution.
• State Gauss-Markoff linear model.
• Define BLUE.
• Write down the normal equation of a simple linear regression model.

PART-B

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

11)  Show that the sample variance is consistent estimator for the population variance

of a normal distribution.

12)  Define Completeness with an example. Also, give an example of a family which

is not complete.

13) Let x1, x2, x3… xn, be a random sample from N(µ,σ2) population. Find sufficient

estimator for µ and σ2 .

14) Explain the method of minimum chi-square estimation.

15) Find MLE for the parameter λ of a Poisson distribution on the basis of a sample

of size n and hence, obtain the MLE of P[ X ≤ 1].

16) State and prove Factorization Theorem on sufficient statistics in one parameter

discrete case.

17) Obtain the method of moments estimator for Uniform distribution U(a, b).

(P.T.O)

18) Obtain the Bayes estimator using a random sample of size ‘n’ when

f( x ; q ) =  , x = 0, 1, 2, . . .

and the p.d.f. of q is a two parameter gamma distribution.

PART-C

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

1. (a) State and prove Chapman- Robins Inequality and also mention its importance.

(b) Obtain the minimum variance bound estimator for µ in normal population

N(µ,σ2) where σ2 is known.

1. (a) State and prove Rao-Blackwell Theorem.

(b) Let x1, x2, x3… xn, be random sample from U(0,θ) population obtain

UMVUE for θ.

1. (a) Explain the concept of Maximum Likelihood Estimator

(b) In random sampling from normal population N(µ,σ2) find the MLE for

(i) µ when σ2 is known                   (ii) σ2 when µ is known.

1. (a) Explain the concept of Method of Least Squares.

(b) State and prove the necessary and sufficient condition for a parametric function

to be linearly estimable.

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## Loyola College B.Sc. Statistics April 2012 Distribution Theory Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

FOURTH SEMESTER – APRIL 2012

# ST 4502/ST 4501 – DISTRIBUTION THEORY

Date : 21-04-2012              Dept. No.                                        Max. : 100 Marks

Time : 1:00 – 4:00

PART – A

Answer ALL Questions:                                                                                                       (10 x 2 =20)

1. 1. Find the value of for which the function is a probability density function.
2. Define: Correlation coefficient.
3. Write down the density function of hyper geometric distribution.
4. Obtain the mean of geometric distribution.
5. Write down the density of bivariate normal distribution.
6. Define: Chi-square statistic
7. State any two properties of t-distribution
8. Write down the distribution function of if .
9. Obtain the density function of the nth(largest) order statistic when a sample of size n is drawn from a

population with pdf

1. Define: Stochastic convergence.

PART – B

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

1. Let and have the joint pdf  described as follows:
 (0,0) (0,1) (1,0) (1,1) (2,0) (2,1) 1/18 3/18 4/18 3/18 6/18 1/18

Obtain the marginal probability density functions and the conditional expectations

1. Let and have the joint pdf

Examine whether the random variables are independent.

1. Establish the lack of memory property of geometric distribution.
2. State and prove the additive property of Binomial distribution.
3. Find the median of Cauchy distribution with location parameter and scale paramter  .
4. Obtain the moment generating function of standard normal distribution.
5. Show that ratio of two independent standard normal variates has Cauchy distribution.
6. State and prove Central limit theorem for iid random variables.

PART – C

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

1. (a) Derive the mean and variance of Poisson distribution.

(b) Let and have a bivariate binomial distribution with  and

. Obtain

1. (a) Write down the density function of two parameter gamma distribution. Derive its moment

generating function and hence the mean and variance of the distribution.

(b) Let  . Find the density function of

1. (a) Derive the distribution of t-statistic.

(b) Derive the sampling distribution of sample mean from a normal population.

1. (a) Find where  is the largest order statistic based on a sample of size four from a

population with  pdf

(b) Obtain the limiting distribution of nth order statistic based on a sample of size n drawn from

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## Loyola College B.Sc. Statistics April 2012 Design & Analysis Of Experiments Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

SIXTH SEMESTER – APRIL 2012

# ST 6603/ST 6600 – DESIGN & ANALYSIS OF EXPERIMENTS

Date : 16-04-2012              Dept. No.                                        Max. : 100 Marks

Time : 1:00 – 4:00

PART – A

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

1. Define: Linear contrast and give an example of the same.
2. Write down the mathematical model of a LSD.
3. Mention how the principle of randomization is achieved in a completely randomized design.
4. Give the skeleton ANOVA table for one-way classification.
5. State the number of degrees of freedom associated with error in the analysis of  6 x 6 LSD.

1. When do you recommend RBD?
2. Write all possible treatment combinations in a design.
3. Mention the difference between Partial and Total confounding.
4. Write the factorial effect corresponding to in design.
5. Write down all possible first order interactions in a 23 experiment.

PART – B

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

1. Write a descriptive note on Local Control.
2. Obtain the Least Squares Estimators of the parameters of a RBD.
3. Describe the linear model suitable for one way classified data and estimate the parameters in it.
4. Derive the formula for estimating the missing value in a RBD when one observation is missing.
5. Present the ANOVA table for a k x k LSD and explain the test for equality of treatment effect.
6. Explain Yates method of computing  in the case of a design.
7. Explain the terms: Quadratic Effect and Linear Effect in the case of a factorial design involving two factors with three levels each.
8. State and prove Fisher’s inequality associated with BIBD.

(P.T.O)

PART – C

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

1. Describe in detail the preparation of layout for a Randomized Block Design and the steps involved in its analysis.
2. Describe fully the analysis of a factorial design.
3. Explain Balanced Incomplete Block Design and describe in detail the intra-block analysis for the same.
4. (a) Explain the analysis of experimental design wherein the highest order interaction effect

is totally confounded.

(b) Explain : (i) Duncan’s Multiple Range Test          (ii) Cochran’s Theorem.

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## Loyola College B.Sc. Statistics April 2012 Computational Statistics Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

FIFTH SEMESTER – APRIL 2012

# ST 5507 – COMPUTATIONAL STATISTICS

Date : 03-05-2012              Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

Answer any THREE of the following questions:

(a) A Textile manufacturer keeps a record of the defects that occur on the material by noting down the number of defects observed per 500 meter of the cloth. The data collected from 180 such pieces of cloth are reported below.

 No. of Defects 0 1 2 3 4 5 No. of Pieces 10 25 62 54 21 8

Fit a Poisson distribution to the number of defects per 500 meter length and test for

goodness of fit at 5% level of significance.

(b) Data on the life-time of 250 machines are given below:

 Life Time (in hrs) 0-1 1-2 2-3 3-4 4-5 5-6 6-7 7-8 >8 No. of failed machines 85 51 35 24 18 15 12 7 3

Test at 5% level of significance whether the Life Time random variable follows

exponential distribution with p.d.f. f(x) = θe–θ x , x > 0.

(15 +18)

• (a) A population consists of 5 units with ‘y’ values 1, 4, 6, 9, 12. Enlist all possible simple random samples of size 3 that can be drawn without replacement and verify the results E() = and E(s2) = S2.

(b) A population with 300 units is divided into three strata. A stratified random sample

was drawn and the observed values in the sample are reported below:

 Stratum No. Stratum Size Sample observations 1 2 3 75 100 125 21, 26 32, 35, 37 40, 48, 49, 45

Obtain the estimate and get an estimate of its variance from the sample data.

(16 + 17)

• (a) Compute index number for the given data using the following methods (i) Laspeyre’s

method,  (ii) Passche’s method and (iii) fisher’s ideal formula                            (8)

 Item (Rs.) Base year Current year Price (in Rs) Expenditure Price (in Rs) Expenditure Food 10 600 20 1000 Rent 8 400 4 480 Clothing 8 480 12 600 Fuel 25 650 24 720 Others 16 640 20 960

(b) Change the base year 1996 to 2000 and rewrite the series of index numbers in the

following data:

 Year 2000 2001 2002 2003 2004 2005 2007 2008 2009 Index 100 112 125 160 140 165 170 175 182

(5)

(c) Calculate the seasonal indices by the method of least squares from the following data:

(Multiplicative model)                                                                                            (20)

 Exports of cotton textiles (million Rs.) Year I II III IV 2001 71 65 79 71 2002 76 66 82 75 2003 74 68 84 80 2004 76 70 84 79 2005 78 72 86 85

• (a) On any given day at a warehouse, 14 trucks are loaded with a particular product.

It is claimed that the median weight m of each load of the product is 39,000 pounds.

On a particular day, the following observations were obtained:

41,195        39,485         41,229        36,840         38,050          40,890     35720

38,345       34,930          39,245        31,031         40,780         38,050      30,906

Test the null hypothesis H0 : m = 39,000  against the one-sided alternative  hypothesis

H1 : m < 39,000 using  the critical region C = { y | y ≥ 9 } where ‘y’ is the number of observations in the sample that are less than  39,000. Find the significance level α for the critical region C.  Also find the p – value of this test.

(13)

(b)  A vendor produces and sells low-fat milk powder to a company that

uses it to produce health drink formulae.  In order to determine the fat

content of the milk powder , both the company and the vendor take a

sample from each lot and test it for fat content in percent.  Ten sets of paired

test results are as follows:

 Lot Number Company Test Results (X) Vendor test results( Y)                                                 Vendor Test Results (Y) 1 0.50 0.79 2 0.58 0.71 3 0.90 0.82 4 1.17 0.82 5 1.14 0.73 6 1.25 0.77 7 0.75 0.72 8 1.22 0.79 9 0.74 0.72 10 0.80 0.91 11 0.92 0.74 12 0.58 0.55

Test the hypothesis H0 : p  =  P[X > Y]  =   against the one – sided alternative  H1 : p >

using the critical region  C = { w | w ≥ 7 },  where ‘w’ is the number of pairs for which

Xi – Yi  > 0. Find the significance level α  and p – value of this test.                      (20)

• (a) Measurements  of the fat content of two kinds of food item , Brand X  and Brand Y

yielded the  sample data :

Brand  X :   13.5      14.0    13.6   12.9     13.0    14.2     15.0    14.3     13.8

Brand Y :    12.9      13.0    12.8   143.5   12.7    15.0     18.7    11.8    14.3

Test  the null hypothesis μ= μ2   against  μ1  μ2  at 5% level of significance.

(9)

( b)       Two random samples drawn from two normal populations are :

Sample I     :    23      15       25       27      23     20       18      24     25

Sample II    :    27      33       45       35      32     35       33      28     41      43

Test whether  the two populations have the same  variances.  Use 5% significance

level.

(8)

(c)  Seven coins were tossed and the number of heads noted. The experiment was repeated

130 times  and the following distribution was obtained.

No. of heads :   0          1          2             3            4             5              6             7

Frequency    :   7           6          19           35        30           23             9             1

Fit a binomial distribution to the given data and test the goodness of fit at 1% level of

significance.                                                                                                       (16marks)

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## Loyola College B.Sc. Statistics April 2012 Applied Statistics Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

FIFTH SEMESTER – APRIL 2012

# ST 5506/ST 5502 – APPLIED STATISTICS

Date : 30-04-2012              Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

PART – A

Answer ALL the questions:                                                                                           (10 x2 = 20)

1. What are index numbers?
2. State Time Reversal Test.
3. What are the components of a time series?
4. Define Multiplicative Time Series model
5. Define Crude Birth Rate.
6. Distinguish between gross reproduction rate and net reproduction rate.
7. Give the meaning of multiple correlation coefficient.
8. Write down the expression for .
9. Mention the role of NSSO.
10. Mention the use of Statistics in livestock and poultry industry.

PART – B

Answer any FIVE Questions:                                                                                        (5 X 8 = 40)

1. Explain the concept of Splicing and Deflating of index numbers.
2. Explain the steps involved in the construction of index numbers?
3. Explain the method of moving averages in estimation of trend.
4. Explain ratio to trend method of estimating seasonal variation.
5. Describe in detail various rates associated with fertility.
6. Explain how vital statistics is obtained in India.
7. Prove the relation .
8. Describe the functions of CSO.

PART – C

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

1. (a) Define : Fisher’s Index number. Show that it is an Ideal Index number.

(b) Write a descriptive note on Consumer Price Index number.

1. (a) Find the trend component in the following data with the help of 3 yearly moving averages.

Year:            1978  1979  1980 1981 1982 1983 1984 1985 1986 1987 1988 1989

Production:    19      22      25     27     29     30     32      34     37     41    44     45

(in tonnes)

(b) Explain the method of Link Relatives.

1. (a) Write a short note on Season Variation.

(b) The population size of a country are given below:

Year :              1960    1970    1980    1990    2000    2010

Population :      22       27       36         48        59       72

(in crores)

Fit an exponential trend and estimate the population for the year 2014.

1. Write short notes on the following:

(a) Chain Index Numbers

(b) Measurement of Mortality

(c)  National Income Statistics

(d) Partial Correlation.

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## Loyola College B.Sc. Statistics April 2012 Basic Sampling Theory Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

THIRD SEMESTER – APRIL 2012

# ST 3504/ST 3502/ST 4500 – BASIC SAMPLING THEORY

Date : 26-04-2012              Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

PART – A

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

1. Define Population and sample.
2. Explain sampling frame and give an example.
3. Define simple random sampling without replacement.
4. Distinguish between a questionnaire and schedule.
5. In SRSWOR, find the number of samples of size 3 that can be drawn from a population of size 15.
6. Distinguish between bias and error.
7. Explain stratified random sampling.
8. What are the merits of stratified random sampling?
9. Define linear systematic sampling.
10. What is meant by circular sampling?

PART – B

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

1. Discuss briefly the basic principles of a sample survey.
2. Explain Lottery Method and Random Number Table Method of unit selection.
3. In SRSWOR, prove that the sample mean is unbiased estimator of population mean. Also find its variance.
4. In SRSWR, prove that .
5. Explain modified systematic sampling and derive the expression for variance of the sample mean.
7. Explain cumulative total method of PPS selection.
8. In usual notations, prove that the systematic sample mean is more precise than the mean of SRSWOR if .

PART – C

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

1. (a) Discuss the advantages of sampling over completer enumeration.

(b) A population contains 12 units with y-values arranged according to their labels as

3, 5, 4, 7, 8, 2, 9, 12, 11, 15, 13, 14. List all possible linear systematic samples of

size 4.

1. (a) Derive the variance of Hansen-Hurwitz estimator for population total.

(b) Explain proportional allocation and optimum allocation.

1. Prove that when we compare stratified random sampling with SRS                              .
2.  Compare simple random sampling and linear systematic sampling in the presence of linear trend.

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

THIRD SEMESTER – APRIL 2012

# ST 3104/3101 – BUSINESS STATISTICS

Date : 28-04-2012              Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

SECTION A

Answer ALL questions.                                                                                    (10 x 2 =20)

1. Define median. Give an example.
2. Write any two applications of statistics in business.
3. Find the  mode: 3,5,6,5,6,7,2,8,9,6,7,8,10,6.
4. Write down the formulae for Regression equations X on Y and Y on X.
5. Define correlation.
6. Mention any two uses of Index numbers.
1. What is Time Series?
1. Write down the formula for Karl Pearson’s coefficient of Skewness
2. Define Transportation Problem.
3. List out Methods of finding an Initial Basic Feasible Solution (IBFS).

SECTION B

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

1. Draw a Histogram and Frequency Polygon for the following data:
 Class interval 500-509 510-519 520-529 530-539 540-549 550-559 560-569 Frequency 8 18 23 37 47 26 16

1. Write down the merits and demerits of statistics.
2. Calculate Q.D and coefficient of Q.D for the given data:
 X 10 20 30 40 50 80 90 F 4 7 15 18 7 2 5

1. Find coefficient of rank correlation between the variables X and Y.
 Weight of fathers 65 66 67 68 69 70 71 Weight of mothers 67 68 66 69 72 72 69

1. Construct the Price index numbers to the following data by using the method of

(i) Laspeyre’s (ii).Paasche’s (iii). Marshall-Edgeworth (iv). Fisher’s Ideal index number

 Commodities 2010   P0               Q0 2011   P1               Q1 A 10 6 15 5 B 12 10 15 10 C 18 5 27 3 D 8 5 12 4

1. Calculate Karl Pearson’s Coefficient of Skewness:
 Size 1 2 3 4 5 6 7 Frequency 10 18 30 25 12 3 2

1. Solve the following Assignment Problem, given the cost involved for each machine.
 Works Machines M1 M2 M3 M4 W1 15 6 7 8 W2 3 13 7 6 W3 8 9 4 10 W4 3 5 7 11

1. Fit a Straight line to the following data.
 X 2 4 6 8 10 Y 4 3 5 3 6

SECTION C

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

1. (i) Find the Mean and Standard Deviation from the following data:
 Class interval 20-30 30-40 40-50 50-60 60-70 70-80 80-90 frequency 3 61 132 153 140 51 2

(ii) Two cricketer scored the following runs in seven matches. Find who is more consistent                 player.

 M.Hussey 67 29 95 83 44 101 72 V.Kholi 35 71 108 40 64 94 88

1. Obtain the Initial Basic Feasible Solution and the cost of the Transportation Problem by        Using (i) North-West Corner Rule, (ii) Least Cost method and (iii) Vogel’s Approximation Method.
 Origin Destination D1 D2 D3 Supply O1 4 9 6 8 O2 5 5 3 11 O3 7 6 10 7 O4 3 8 4 17 Demand 10 12 21 43

1. The following table gives the age of cars of a certain make and annual maintenance costs.
 Age of cars in years 2 4 6 8 10 12 Maintenance cost in Rs.(’00) 10 20 30 50 62 74

(i)  Find the two Regression Equations.

(ii) Estimate the likely Age of cars in years when Maintenance cost in Rs 2500

(iii) Calculate the correlation between Age of cars in years and Maintenance cost.

1. Find the seasonal variations by the Link Relative Method to the following data
 YEAR QUARTER 2007 2008 2009 2010 2011 I 30 35 31 31 34 II 26 28 29 31 36 III 22 22 28 25 26 IV 31 36 32 35 33

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## Loyola College B.Sc. Statistics April 2012 Applied Stochastic Processes Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

FIFTH SEMESTER – APRIL 2012

# ST 5400 – APPLIED STOCHASTIC PROCESSES

Date : 27-04-2012              Dept. No.                                        Max. : 100 Marks

Time : 1:00 – 4:00

Section-A                                                     10×2=20 marks

• Define the term Stochastic
• Define State space with an example
• What is meant by Martingales?
• Define the period of a state of a Markov Chain.
• When is state “I” communicate with state “j”?
• What is meant by transient state?
• What is meant by Stationary Increments?
• Define irreducible Markov Chain with an example
• Explain the term transitivity.
• Define mean recurrence time.

Section-B                                                                                  5×8=40 marks

11) Discuss the  applications of   Stochastic processes  with suitable illustrations..

12) Explain the Gambler’s ruin  problem with the TPM .

13) Explain the one dimensional random walk problem with the TPM

14) If ‘’I” communicate with “j” and “I” is recurrent then show that “j” is also recurrent.

15) Discuss in detail the higher order transition probabilities with suitable illustration.

16) Find the Stationary distribution of a Markov Chain with States 1,2 and 3 with the following

TPM

17)  Show that recurrence is a class property.

18) Explain two dimensional random walk..

Section-C                                                                                  2×20=40 marks

19a)  If the  probability of a dry day (state-0) following a rainy day (state-1)is 1/3, and that of a rainy day following a dry day is  ½.   Find

1. Probability that May 3 is a dry day given that May first is a dry day.
2. ii) Probability that May 5 is a rainy day given that May first is a dry day.

19b)  Discuss in detail Pure Birth process.   (12 + 8 Marks)

20a) State and prove Chapman-Kolmogrov equation.

20b) Discuss in detail the applications of basic limit theorem of Markov Chains. (12 + 8 Marks)

21) A white rat is put into the maze consisting of 9 compartments. The rat moves through the compartment at random. That is there are k ways to leave a compartment. The rat chooses each of the move with probability1/k.

1. a) Construct the Maze

b)The Transition probability matrix

1. c) The equivalence class
2. d) The periodicity (5+5+5+5 Marks)

22) Diabetes disease in any  Society (with different classes of people ) often considered as a family disease which occurs as  successive generations in a family can be regarded as a Markov Chain. Thus the disease of the children is assumed to be depended only on the disease of the parents. The TPM of such model is as follows:

Children’s Class

Mild    Moderate   Severe

Mild                      0.40.        0.50         0.10

Parent’s Class    Moderate                0.05         0.70          0.25

Severe                     0.05         0.50          0.4

Find a) What proportion of   people are Moderate class in the long run suffering from diabetes?

1. b) Show that the MC is recurrent  (12 + 8 Marks)

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## Loyola College B.Sc. Statistics April 2012 Actuarial Statistics Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

FIFTH SEMESTER – APRIL 2012

# ST 5404 – ACTUARIAL STATISTICS

Date : 27-04-2012              Dept. No.                                        Max. : 100 Marks

Time : 1:00 – 4:00

ST-5404  actuarial STATISTICS                  MAX: 100 Marks

Section – A

(Answer all the questions)                                    (10 x2 =20)

1. What is the present value of Rs.5,000 receivable at the end of 75 years, the rate of interest being taken as 6 % p.a?
2. Find the nominal rate p.a convertible quarterly corresponding to an effective rate of 8% p.a.
3. Show that
4. Give the formula for an and Sn
5. Evaluate v60 @ 6.2%
6. Write an expression 10P42, 10 │ 5P
7. Define d
8. What is a temporary assurance?
9. What is the need for a commutation function?
10. Expand Sx in terms of  Dx

Section – B

(Answer any five questions)                                    (5 x 8 =40)

1. A sum of Rs.2000 is invested at a rate of interest of 5%p.a. After 7 years, the rate of interest was changed to 5% p.a. convertible half yearly. After a further period of 3 years, the rate was again changed to 6%p.a. convertible quarterly. What is the accumulated value at the end of 15 years from the commencement?

1. Define the following:
• Annuity
• Immediate annuity
• Annuity due
• Deferment period

1. Calculate the present value of a deferred annuity payable for 10 years certain, the first payment falling due at the end of 6 years from the present time. The annuity is payable at the rate of Rs. 100 p.a. for the first 5 years and Rs.200 p.a. thereafter.

(a5 = 4.3295,  a10 = 7.7217,  a15 = 10.3797)

1. A fund is to be set up out of which a payment of Rs.100 will be made to each person who in any year qualifies for membership of a certain profession. Assuming that 10 persons will qualify at the end of one year from now, 15 at the end of 2 years, 20 at the end of 3 years, and so on till the number of qualifiers is 50 per annum. When it will remain constant, find at 5% p.a. effective what sum must be paid into the fund now so that it sufficient to meet the outgo.

1. Derive the expression to find the present value and accumulated value of Increasing

annuity where in the successive installment form  a geometric progression.

1. Find the office annual premium for a capital redemption assurance policy of Rs. 3000 redeemable at the end of 20 years, assuming interest rate of 6% and a loading of 8% of office premium.

1. Using the LIC ( 1970 – 73 ) Ultimate table find the following  probabilities

• that a life aged 35 dies within 12 years
• that a life aged 40 dies not earlier than 12 years and not later than 15 years
• that a life aged 52 survive 12 years
• that a life aged 52 will not die between age 65 and 70      ( 2+2+2+2)

1. Explain Pure Endowment Assurance.

Section – C

(Answer any two questions)                               ( 2 x 20 =40)

1. Explain the various types of annuity and derive the expression for present value and accumulated value of an immediate annuity certain and deferred annuity certain.

1. a)A deposit annually Rs. 200 p.a. for 10 years, the first deposit being made one year from now; and after 10 years the annual deposit is enhanced to Rs. 300 p.a. Immediately after depositing the 15 payment he closes his account. What is the amount payable to him if interest is allowed at (i) 6% p.a. (ii) 9% p.a.?
2. b) What is the principle of insurance? How has endowment type assurance

emerged?

1. a) Fill in the blanks in the following portion of a life table
 Age  X lx dx qx px 10 1000000 0.00409 11 0.00370 12 0.99653 13 0.99658 14 0.00342

1. b) Using commutation function based on LIC ( 1970 – 73) ultimate mortality table at 6% interest calculate for a person aged 40

• The present value of Whole Life Assurance of 10000
• The present value of Double Endowment Assurance of 10000

for 15 years term . Also calculate present value of Endowment Assurance and Pure Endowment of each for Rs. 10000 for 15 years term.

1. a) Explain Rx ,Mx,Dx and obtain expression for ( IA) x : n

b)The following particulars are given:

 X 25 26 27 28 29 30 lx 97380 97088 96794 96496 96194 95887 dx 292 294 298 302 307 313

Calculate ignoring interest and expenses:

• The value of Temporary Assurance of Rs. 1000 for 2 years for a person aged 25.
• The value of Endowment Assurance benefits of Rs. 1000 for 4 years to a person aged 25.
• The value of a Pure Endowment of Rs. 600 for a person aged 27 receivable on attaining age 30.

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## Loyola College B.Sc. Statistics Nov 2012 Testing Of Hypotheses Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

FIFTH SEMESTER – NOVEMBER 2012

# ST 5505/ST 5501 – TESTING OF HYPOTHESES

Date : 03/11/2012             Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

PART – A

Answer ALL Questions:                                                                                           ( 10 x 2 = 20 Marks )

1. Distinguish between Simple and Composite hypotheses.
2. Define Best Critical Region.
3. Define Exponential Distribution.
4. When do you call a test uniformly most powerful?
5. Define SPRT for testing Ho against H1.
6. State the ASN function for the SPRT for testing Ho: q = q0 against H1: q = q1.
7. What do you mean by one-tailed and two-tailed tests?
8. State the assumptions for Student’s t-test.
9. Mention the assumptions associated with Non-parametric tests.
10. State the situations where Sign test can be applied.

PART – B

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

1. Explain the concept of critical region.

12 Define and elaborate two types of errors in testing of hypothesis.

1. Discuss the general approach of likelihood ratio test.
2. Find the LRT of Ho: q = q0 against H1: q ≠ qo based on sample of size 1 from the density

f ( x, q ) = 2 ( q – x ) / q2  ,  0 < x < q

1. Explain the concepts
2. i) Level of Significance
3. ii) Null and Alternative hypotheses.
4. A manufacturer of dry cells claimed that the life of their cells is 24.0 hours. A sample of

10 cells had mean life of 22.5 hours with a standard deviation of 3.0 hours.  On the basis of

available information, test whether the claim of the manufacturer is correct.

17  In a breeding experiment, the ratio of off-spring in four classes was expected to be 1:3:3:9.

The experiment yielded the data as follows:

Classes                            AA           Aa          aA             aa

No.of offsprings:               8              29          37           102

Test whether the given data is in agreement with the hypothetical ratio.

1. Use the sign test to see if there is a difference between the number of days required to collect

an account receivable before and after a new collection policy. Use the 00.5 significance level

Before:  33  36  41  32  39  47  34  29  32  34  40  42  33  36  27

After  :  35  29  38  34   37  47  36  32  30  34  41  38  37  35  28

PART – C

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

19 a) State and Prove Neymann-Pearson Lemma.

1. b) A sample of size 1 is taken from density

f ( x, q ) = 2 ( q – x ) / q2  ,  0 < x < q

= 0   else where

Find an Most Powerful test of Ho: q = q0 versus H1: q = q1 ;  q0 > q1  at level α .

20 a) Describe the sequential procedure for testing Ho: q = q0 against H1: q ≠ q1 where q is the

parameter  of the Poisson distribution.

1. b) The heights of ten children selected at random from a given locality had a mean 63.2 cms

and variance 6.25 cms.  Test at 5 % level of significance the hypothesis that the children of

the given locality are on the average less than 65 cms in all. Given for 9 degrees of freedom

P( t.> 1.83) = 0.05.

1. a) Explain Chi-square test of Goodness of fit.

1.  b)  The following table gives the number of aircraft accidents that occurred during the seven

days of the week.  Find whether the accidents are uniformly distributed over the week.

Days                   :  Mon     Tue    Wed    Thur    Fri     Sat    Total

No.of accidents  :    14        18       12        11      15      14      84

1. a) Find 99 % confidence limits for the parameter l in Poisson distribution.

1. b) Apply Median Test for the following data:

X:     27   31   32   33   34   29   35

Y:     28   30   30   24   25   26

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## Loyola College B.Sc. Statistics Nov 2012 Testing Of Hypotheses Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

FIFTH SEMESTER – NOVEMBER 2012

# ST 5505/ST 5501 – TESTING OF HYPOTHESES

Date : 03/11/2012             Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

PART – A

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

1. Distinguish between Simple and Composite hypotheses.
2. Define Best Critical Region.
3. Define Exponential Distribution.
4. When do you call a test uniformly most powerful?
5. Define SPRT for testing HO against H1.
6. State the ASN function for the SPRT for testing Ho: q = q0 against H1: q = q1.
7. What do you mean by one-tailed and two-tailed tests?
8. State the assumptions for Student’s t-test.
9. Mention the assumptions associat

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