## Loyola College B.Sc. Statistics Nov 2008 Actuarial Statistics Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

# BA 17

FIFTH SEMESTER – November 2008

# ST 5404 – ACTUARIAL STATISTICS

Date : 12-11-08                       Dept. No.                                          Max. : 100 Marks

Time : 9:00 – 12:00

PART-A

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

1. Define immediate perpetuity, perpetuity due.
2. The amount with compound interest of a certain principal at 5% pa is Rs3969. Find the  principal

when the period is 2 years.

1. Find the nominal rate p.a convertible half-yearly corresponding to an effective rate of  8% p.a.
2. The accumulated value of a certain annuity paid after 8 years at the rate of 8% is 2866.35.  Find the

present value.

1. Explain deferred annuity due.
2. Define Lx .
3. Explain Ax .
4. Explain the need for a life table.
5. What is the need for a commutation function ?
6. Expand Sx in terms of Dx  .

PART-B

1. A has taken a loan of Rs2000 at rate of interest 4% pa payable half yearly. He repaid Rs.400 after

2 years,Rs.600 after a further 2 years and cleared all outstanding dues at  the end of 7 years from

the commencement of the transaction. What is the final   payment made by him?

1. Derive the formula for accumulated value and present value of annuity certain due.
2. Derive the formula for an increasing annuity .
3. Find the present value of an immediate annuity of Rs.600 p.a payable quarterly for 20 years at a

rate of 6% p.a payable half yearly.

1. Find the probability that of 2 persons A and B aged 30 and 35 respectively

i.)both die before 55.

ii.)both die after 60.

iii.)A dies before 65 while B dies after 60.

iv.)Atleast one of them survives to 70.

1. Obtain the expressions for a x: n and  ( Ia )x : n   .
2. Calculate the net annual premiums for sum assured of Rs.5000 for the following

assurances on (40)

a.)pure endowment assurance for 20 years.

b.)Temporary assurance for 20 years.

1. Obtain the formula for an and Sn.

PART-C

1. a) Complete the following life table.

Age                   lx                dx              qx               Lx

10               1000000             –            .00409             –

11                    –                     –           .00370              –

12                    –                     –           .00347              –

13                    –                     –           .00342              –

1. b) An employee of an institution has to retire at the age of 58.A gratuity benefit of

one months salary for each year of service subject to a maximum benefit of 15

months salary is payable to an employee on retirement or death , as the case may

1. Find the probability that:

i.)full gratuity  benefit will be payable to a person aged 35, who has just now

completed 5 years of service.

ii.)the gratuity benefit will not exceed 10 months salary .

iii.)the gratuity benefit will be atleast 12  months salary.

iv.)the employee earns atleast 12months salary as gratuity benefit payable at

death.

1. a) A loan of Rs.5000 is to be repaid with interest at 8% p.a be means of an

immediate annuity for 10 years. Find the yearly installment. What will be the

principal and interest contained in the 5th installment? What will be the principal

outstanding immediately after the 8th payment is made?

1. b) Find the present value of an immediate annuity of Rs.240 p.a payable in equal

monthly installments for 10 years certain at nominal interest of 8% p.a convertible

half yearly.

1. a) A person aged 30 years approached a life office for special type of policy  providing for the

following benefits.

i.)Rs.1000 on death during the first 5 years.

ii.)Rs.2000 on death during the next 15 years.

iii.)survival benefit of Rs.500 at the end of the 5th year .

iv.)Further payment of Rs.2000 on survival of 20 years.

Find the annual premium assuming that the premium paying term is 20 years.

1. b) Derive the expression for x: n and (IA )x: n .

• a) A had decided to invest Rs.500 at the end of each year. He did so far 7 years.

Then there was a gap of 4 years. He could again invest Rs.500 p.a for the next 4

years beginning from the end of the 12th year. Find the amount to his credit at the

end of the 15th year assuming interest rate of 9% p.a.

1. b) A payment of Rs.P falls due at the end of every γ years .Find at the rate of

interest of i  p.a the present value of the payments to be paid during n years ( n is

an exact multiple of γ).

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## Loyola College B.Sc. Statistics April 2009 Statistical Process Control Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

 YB 30

B.Sc. DEGREE EXAMINATION – STATISTICS

SIXTH SEMESTER – April 2009

# ST 6602 – STATISTICAL PROCESS CONTROL

Date & Time: 23/04/2009 / 9:00 – 12:00   Dept. No.                                                  Max. : 100 Marks

PART A

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

1. Define Total Quality Management.
2. Mention the basic concepts in quality improvement.
3. How will you model the process quality?
4. Define quantile plot.
5. Distinguish between control charts for attributes and control charts for variables.
6. What are the advantages of control charts?
7. Define the purpose of process capability analysis.
8. What are slant control charts?
9. Mention an application where continuous sampling plan can be used.
10. Explain multiple sampling plan for attributes.

PART B

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

1. Examine the need for quality control techniques in production.

1. Explain the chance and assignable causes of variation in the quality of manufactured product.

1. The sample given below represents the number of defectives found in batches of a production line. Construct a stem and leaf display with stem labels 1,2,3,4,5,6,7,8,9 and leaves ordered.
 258 639 739 839 579 679 588 688 654 673 838 412 638 619 369 759 859 679 779 628 728 659 471 571 671 534 693 738 106 206 465 608 708 808 908 998 639 739 489 674 556 656 329 567 509 523 428 528 628 495

1. What is a control chart? Explain the basic principles underlying the control charts.

1. A machine produces spark plugs to tolerance limits of 25 thousandths of an inch ± 2 thousandth of an inch. Plugs outside this range would give erratic running of the engine. It is decided to set up control charts for the machine. Records reveal that the average range for sample of 5 items is 1 and the mean of the means is 25.1. Setup the mean and range charts.

(d2 = 2.326, D3 = 0, D4 = 2.11)

1. Explain the basic principles underlying the slant control charts.

1. Explain the terms: (i) Producer’s and consumer’s risks

(ii) AQL and LTPD

1. Discuss the relative merits and demerits of single and double sampling plans.

PART C

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

1. a) Explain the need and utility of Total Quality Management.                                  (10)

1. b) Batches of 100 components were taken at fixed interval of time from a production line and tested. The following figures are the number of components found to be non-conforming in each of the batches:
 4 3 2 0 7 5 2 4 1 3 4 6

Calculate the mean proportion rejected. Draw a quality control chart for samples of 200 such that the inner limit is equal to the mean plus one standard error and the outer limit is equal to mean plus two standard error.                                                                        (10)

1. a) Explain histogram and frequency distribution as methods of describing quality variation.

(10)

1. b) Draw a suitable control chart for the following data pertaining to the number of coloured threads considered as defects in 15 pieces of cloth in a certain synthetic fibre and state your conclusions:
 7 12 3 20 21 5 4 3 10 8 0 9 6 7 20 (10)

1. a) Explain the underlying principle and working of CUSUM chart                           (10)

1. b) Explain in detail the item by item sequential sampling plan (10)

1. a) What is meant by acceptance sampling procedures? What are its advantages?     (10)

1. b) Describe single sampling plan. Obtain the OC and AOQ curves for this plan. (10)

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## Loyola College B.Sc. Statistics April 2009 Statistical Methods Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

 YB 01

FIRST SEMESTER – April 2009

# ST 1502/ST 1500 – STATISTICAL METHODS

Date & Time: 20/04/2009 / 1:00 – 4:00  Dept. No.                                                      Max. : 100 Marks

PART – A

Answer ALL questions:                                                                                   10 x 2 = 20

1. States any two applications of statistics.
2. Distinguish between primary and secondary data.
3. What are the characteristics of a good measure of central tendency?
4. Find the coefficient of variation from the following data.

.

1. State the principle of least squares.
2. Write the normal equations for fitting the curve .
3. The ranks of two attributes in a sample are given below. Find the correlation between them.
4. If and are the regression coefficients of y on x and x on y respectively, show that.
5. Check whether A and B are independent given the data:

N=10,000,       (A)=4500,        (B)=6000,        (AB)=3150

1. Distinguish between correlation and regression.

PART – B

Answer any FIVE questions:                                                               5 x 8 = 40

1. Explain classification and tabulation of data.
2. Draw less than and more than ogives from following data:
 Profits: (Rs. Lakhs 10-20 20-30 30-40 40-50 50-60 No. of Companies: 6 8 12 18 25 Profits: (Rs. Lakhs) 60-70 70-80 80-90 90-100 No. of companies: 16 8 5 2
1. Calculate the mean, median and hence mode from the following data:
 Mid pt: 15 25 35 45 55 65 75 85 Frequency: 5 9 13 21 20 15 8 3
1. For a moderately skewed data, the arithmetic mean is 200, the coefficient of variation is 8 and Karl Pearson’s coefficient of skewness is 0.3. Find the mode and median.
2. Fit a straight line trend for the following data:
 Year: 1980 1981 1982 1983 1984 1985 1986 Y: 83 60 54 21 22 13 23
1. Show that the coeffient of correlation lies between -1 and +1.
2. In a group of 800 students, the number of married students is 320. But of 240 students who failed, 96 belonged to the married group. Find out whether the attributes of marriage and failure are independent.
3. Given the following data, find the two regression equations:

PART – C

Answer any TWO questions:                                                               2 x 20 = 40

1. a) Explain the scope and limitations of statistics.
2. b) The following table gives the frequency, according to groups of marks obtained by 67 students in an intelligence test. Calculate the degree of relationship between age and intelligence test.
 Age in years Test marks 18 19 20 21 Total 200-250 4 4 2 1 11 250-300 3 5 4 2 14 300-350 2 6 8 5 21 350-400 1 4 6 10 21 10 19 20 18 67
1. a) Define measure of dispersion. Prove that the standard deviation is independent of change of origin but not scale.
2. b) Find the coefficient of quartile deviation from the following data.
 Wages: 0-10 10-20 20-30 30-40 40-50 No.of Workers: 22 38 46 35 20
1. Calculate the first four moments about the mean and also the values of and from the following data:
 Marks: 0-10 10-20 20-30 30-40 40-50 50-60 60-70 No. of Students: 8 12 20 30 15 10 5
1. a) Fit the curve using the principle of least squares.
2. b) From the following data, calculate the remaining frequencies and hence test whether A and B are

independent.

.

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## Loyola College B.Sc. Statistics April 2009 Statistical Mathematics – II Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

 YB 12

THIRD SEMESTER – April 2009

# ST 3501 / ST 3500 – STATISTICAL MATHEMATICS – II

Date & Time: 06/05/2009 / 9:00 – 12:00     Dept. No.                                                       Max. : 100 Marks

SECTION A

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

1. Define upper sum and lower sum of a function.
2. When do you say that a function is Riemann integrable on [a,b]?
3. Define moment generating function of a continuous random variable.
4. Define improper integrals.
5. State the μ test for convergence of integrals.
6. Define Laplace transform of a function.
7. Let f(x) =    cx 2, 0 < x < 2

0, otherwise

If this is a probability density function, find c.

1. State the second fundamental theorem of integral calculus.
2. State any two properties of Riemann integral.
3. Define absolute convergence of a function.

SECTION B

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

1. For any partition P  on [a, b], prove that m (b – a) ≤ L (P, f) ≤ U (P, f) ≤ M (b – a).

Where m =  , M = and f is a bounded function on [a,b].

1. Let f(x) = x 2, 0 ≤ x ≤ 1. By considering partitions of the form  P n =

Show that  U (Pn, f) =  L (Pn, f) = 1/3

1. Let X be a random variable with probability density function

f(x) =   1, 0 < x < 1

0, otherwise

Find the moment generating function and hence the mean and variance of X.

1. Show that   (a > 0)   , converges for p > 1 and diverges for p ≤ 1.
2. Discuss the convergence of the following improper integrals:

(i)                                        (ii)

1. Show that  (i)      and      (ii) b (m, n) = b (n, m)
2. Show that L (f + g)(s) = Lf (s) + Lg (s) and Lc f (s) = c Lf (s), where Lf (s) is the Laplace transform of the function f.
3. Evaluate   over the region between the line x = y and the parabola y = x 2.

SECTION C

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

1. (a) Let f, g Є R [a, b], then show that f + g Є R [a, b] and

(b) Let f (x) =      5 x 4, 0 ≤ x < 1

0, otherwise

be the probability density function of the random variable X.

Find (i) P (1/2 < X < 1) (ii) P (-2 < X < 1/2) (iii) P (0 < X < 3/4) (iv) P (1/4 < X < 3)

1. (i) State and prove the first fundamental theorem of Integral calculus.

(ii) Derive the differential difference equations for a Poisson process.

1. (i) Show that b (m, n) =

(ii) If X has the probability density function f (x) = c x 2 e-x, 0 < x < . Find

Expectation of X and variance of X.

1. (a) If  converges absolutely, then show thatconverges.

(b) Discuss the convergence of the following integrals.

(i)    (ii)

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## Loyola College B.Sc. Statistics April 2009 Statistical Mathematics – I Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

 YB 05

SECOND SEMESTER – April 2009

# ST 2502 / 2501 – STATISTICAL MATHEMATICS – I

Date & Time: 23/04/2009 / 1:00 – 4:00 Dept. No.                                                   Max. : 100 Marks

SECTION A

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

1. Define a function.
2. What is a monotonic sequence?
3. State the comparison test for convergence of a series.
4. Define probability generating function of a random variable.
5. How is the variance of a random variable obtained from its moment generating function?
6. Define the derivative of a function at a point.
7. What do you mean by probability distribution function of a random variable?
8. Does the series      (x ≥ 1) converge?
9. Define rank of a matrix.
10. Define symmetric matrix and give an example.

SECTION B

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

1. If      and  , then prove the following:

1. Prove that the sequence {an} defined by an =     is convergent.

1. Consider the experiment of tossing a biased coin with P (H) = ⅓, P (T) = ⅔ until a head appears. Let X = number of tails preceding the first head. Find moment generating function of X.

1. Show that if a function is derivable at a point, then it is continuous at that point.

1. Verify Lagrange’s mean value theorem for the following function:

f(x) = x2 -3 x + 2 in [-2, 3]

1. When is a set of n vectors said to be linearly independent? Find whether the vectors (1, 0, 0), (4,1,2) and (2, -1, 4) are linearly independent or not.

1. A random variable has the following probability distribution:
 X 0 1 2 3 4 5 6 7 8 p(x) k 3k 5k 7k 9k 11k 13k 15k 17k

(i) Determine the value of k,  (ii) Find the distribution function of X.

1. Find the inverse of  A =

SECTION C

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

1.  (i) Prove that a non decreasing sequence of real numbers which is bounded above is convergent.

(ii) Discuss the bounded ness of the sequence {an}where an is given by,   an =

1. State D’Alembert’s ratio test and hence discuss the convergence of the following series:

1. (i) State and prove Rolle’s Theorem.

(ii) Verify Rolle’s theorem for the following function: f (x) = x2 – 6 x – 8 in [2, 4].

1. (i) A two-dimensional random variable has a bivariate distribution given by,

P(X=x, Y=y) =     , for x = 0,1,2,3 and y = 0, 1. Find the marginal distributions

of X and Y.

(ii) If P(X=x, Y=y) =     , where x and y can assume only the integer values  0,

1 and 2. Find the conditional distribution of Y given X = x.

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## Loyola College B.Sc. Statistics April 2009 Probability And Random Variables Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

 YB 02

FIRST SEMESTER – April 2009

# ST 1503/ ST 1501 – PROBABILITY AND RANDOM VARIABLES

Date & Time: 22/04/2009 / 1:00 – 4:00         Dept. No.                                                       Max. : 100 Marks

PART – A

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

1. Define sample space and elementary event.
2. Four cards are drawn at random from a pack of 5 cards. Find the probability that two are kings and two are queens.
3. State the axioms of probability function.
4. For any two events A and B, show that .
5. Define pairwise and mutual independence of events.
6. The odds that a book in mathematics will be favourably reviewed by 3 independent critics are 3 to 2, 4 to 3 and 2 to 3 respectively. What is the probability that all the three reviews will be favourable?
7. If A and B are two mutually exclusive events show that .
8. A consignment of 15 record players contains 4 defectives. The record players are selected at random, one by one and examined. Those examined are not replaced. What is the probability that the 9th one examined is the last defective?
9. Define a random variable.
10. Define probability generating function.

PART – B

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

1. Five salesmen A, B, C, D and E of a company are considered for a three member trade delegation to represent the company in an international trade conference. Construct the sample space and find the probability that i) A is selected ii) either A or B is selected.
2. For any three non-mutually exclusive events A, B and C, evaluate .
3. Compare the chances of throwing 4 with one die, 8 with two dice and 12 with three dice.
4. State and prove Boole’s inequality.
5. A and B are two students whose chances of solving a problem in statistics correctly are and If the probability of them making a common error is and they obtain the same answer, find the probability that their answer is correct.
6. Let the random variable X have the distribution þþ where þ. For what value of þ is the variance of X, a maximum.
7. The life (in 000’s of kms) of a car tyre is a random variable having the p.d.f.

Find the probability that one of these tyres will last i) at most 10,000 kms ii) at least 30,000 kms.

1. If X and Y are two random variables such that , then show that .

PART – C

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

1. (a) State and prove the multiplication theorem of probability for any ‘n’ events.

(b) In a company, 60% of the employees are graduates. Of these 10% are in sales. Out of the employees who are not graduates, 80% are in sales. What is the probability that

1. i) an employee selected at random is in sales
2. ii) an employee selected at random is neither in sales nor a graduate?
3. a) State and prove Baye’s Theorem.
4. b) Two computers A and B are to be marketed. A salesman who is assigned the job of finding customers for them has 60% and 40% chances respectively of succeeding in case of computers A and B. The two computers can be sold independently. What is the probability that computer A is sold given that he was able to sell atleast one computer?
5. a) State and prove chebychev’s inequality
6. b) A symmetric die is thrown 600 times. Find the lower bound for the probability of getting 80 to 120 sixes.
7. The time a person has to wait for a bus is a random variable with the following p.d.f.

Let the event A be defined as a person waiting between 0 and 2 minutes (inclusive) and B be the event of waiting 0 and 3 minutes (inclusive)

1. Draw the graph of p.d.f
2. Show that and .

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## Loyola College B.Sc. Statistics April 2009 Principles Of Marketing Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS & VIS. COMM.

 KP 13

FOURTH SEMESTER – April 2009

# CO 4204 / 4200 / 3103 / 3100 – PRINCIPLES OF MARKETING

Date & Time: 27/04/2009 / 9:00 – 12:00  Dept. No.                                                 Max. : 100 Marks

PART-A

ANSWER ALL THE QUESTIONS                                                       10 x 2 = 20

1. Define the term Marketing.
2. What is sales promotion?
3. What is meant by product development.
4. Who is a retailer?
5. What are the features of Modern Marketing?
6. What is intensive distribution?
7. Explain undifferentiated marketing.
8. What is meant by personal selling?
9. What is futures market?
10. Define Penetrating Pricing.

PART – B

ANSWER ANY FIVE                                                                              5 x 8 = 40

1. Explain the various objectives of pricing.
2. Describe different approaches to the study of marketing.
3. What are the functions and services provided by wholesalers?
4. Point out different modes of transport. Explain the advantages and limitations of

railway transport.

1. What are the benefits of market segmentation?
2. What is warehousing. What are its functions and advantages?
3. What is meant by marketing of services? How can it be classified?

PART – C

ANSWER ANY TWO QUESTIONS                                                    2 x 20 = 40

1. What is market segmentation? Explain the methods of segmenting the markets.
2. Explain the concept of Product Life Cycle. Describe the various stages of the product

life cycle and indicate the strategies you would adopt at the different stages.

1. Define a market. Explain the seven different classifications of markets.

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## Loyola College B.Sc. Statistics April 2009 Operations Research Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

 YB 29

SIXTH SEMESTER – April 2009

# ST 6601 – OPERATIONS RESEARCH

Date & Time: 21/04/2009 / 9:00 – 12:00    Dept. No.                                                      Max. : 100 Marks

PART A

Answer ALL questions:                                                                                 (10 x 2 = 20)

1. Define Operations Research.
2. How will you identify an infeasible solution in linear programming?
3. Distinguish between Big M and Two phase methods.
4. Write the dual of

Max z = x1 + x2

subject to

x1, x2 ≥ 0

1. What is a traveling salesman problem?
2. Define a transhipment problem.
3. Define a critical path.
4. What are the time estimates used in PERT?
5. What is meant by decision under uncertainty?
6. Define a two-person zero sum game

PART B

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

1. A person requires 10, 12 and 12 units of chemicals A, B and C respectively for his garden. The liquid product contains 5, 2 and 1 units of A, B and C respectively per jar. A dry product contains 1, 2 and 4 units of A, B and C per carton. If the liquid product sells for Rs 3 per jar and dry product sells for Rs 2 per carton, how many of each should he purchase in order to minimize the cost using graphical method?
2. How will you identify unbounded and alternate solutions in a linear programming problem?
3. Explain the dual simplex method of solving a linear programming problem.
4. Four professors are each capable of teaching any one of the following courses. The table below shows the class preparation time in hours by the professors on the topics. Find the assignment of the courses to the professors to minimize the preparation time.
 Professor Linear Programming Queuing Theory Dynamic Programming Inventory Control A 2 10 9 7 B 15 4 14 8 C 13 14 16 11 D 4 15 13 9

1. Distinguish between PERT and CPM.

1. For the following network determine the maximum flow and optimum flow in each link:

1. Find the optimum strategy and value of the game for which there is no saddle point given the payoff matrix of  A:

1. Explain minimax and savage criteria in decision making with suitable examples.

PART – C

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

1. (a) Explain primal-dual relationship in linear programming.

(b) Use penalty method to

Max z = 2x1 + x2 + 3x3

subject to

x1 + x2 + 2x3 ≤ 5

2x1 + 3x2 + 4x3 = 12

x1 , x2 , x3 ≥ 0

1. (a) Solve the following transportation problem with cost coefficients, demand and supply as

given below

(b) Solve using simplex method

Max  Z = 10x1 +  x2 + 2x3

subject to

x1 + x2 – 2x3  £10

4x1 + x2 + x3  £ 20

x1, x2, x3 ≥ 0

1. (a) State the rules for drawing the network diagram.

(b) The following table lists the jobs in a network along with the time estimates.

 Job 1 – 2 1 – 6 2 – 3 2 – 4 3 – 5 4 – 5 6 – 7 5 – 8 7 – 8 Optimistic time (days) 3 2 6 2 5 3 3 1 4 Most likely time (days) 6 5 12 5 11 6 9 4 19 Pessimistic time (days) 15 14 30 8 17 15 27 7 28

(i) Draw the network diagram

(ii) Calculate the length and variance of the critical path

(iii)Find the probability of completing the project before 31 days.

1. (a) A business man has three alternatives each of which can be followed by any one of the four possible events. The conditional payoff in rupees for each action – event combination are as given below:
 Alternative Payoff A B C D X 8 0 10 6 Y -4 12 18 -2 Z 14 6 0 8

Determine which alternative should the business man choose if he adopts (i) Hurwicz Criterion, the degree of optimism being 0.7 (ii) Laplace Criterion

(b) Solve following game graphically:

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## Loyola College B.Sc. Statistics April 2009 Finan.A/C & Financial Statement Analysis Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

 KP 03

B.Sc. DEGREE EXAMINATION –STATISTICS

SECOND SEMESTER – April 2009

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

Date & Time: 25/04/2009 / 1:00 – 4:00  Dept. No.                                                 Max. : 100 Marks

SECTION A

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

1. State the rules of double entry system of bookkeeping.
2. What do you understand by Imprest system of Petty cash book?
3. (i) Earnings per share (EPS) is a

(a) Profitability ratio   (b) Turnover ratio   (c) Liquidity ratio  (d) None of these

.            (ii) In a cash flow statement dividend paid is usually treated as

(a ) application of cash  (b)  source of cash   (c)  loss (d)  gain

1. What is cash discount?
2. Compute the amount of dividend paid during 2008

Proposed dividend on 1-1-08                                     Rs.50,000

Proposed dividend on 31-12-08                                 Rs.40,000

Dividend debited to P& L Appropriation Account    Rs.60,000

1. Calculate Stock turnover ratio:

Opening stock Rs. 29,000:   Closing stock  Rs. 31,000: Purchases Rs. 2,42,000

1. What are ‘Contra Entries’?
2. Calculate the amount of Commission payable to the manager @10% on net profit which amounts to Rs.1,10,000 after charging such commission.
3. Give any two advantages of subsidiary books.
4. What is a cash flow statement?

SECTION B

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

1. On 31st March, 2008 the pass book showed the credit balance of Rs. 10,500.

Cheques amounting to Rs.2,750 were deposited in the bank but only cheque of Rs. 750 had not been cleared up to 31st March.

Cheques amounting to Rs.3,500 were issued, but cheque for Rs.1,200 had not been presented for payment in the bank up to 31st March.

directly from customers Rs.800 and dividend of Rs.130 up to 31st March .      Find out the balance as per cash book.

1. Enter the following transactions in the Purchases and Purchases returns book of Rex

Electrical Co., and post them to ledger

Jan 2009

• Started business with Rs.2,00,000 cash
• Purchased for cash furniture Rs. 2,000
• Bought of Hari

20 Immersion heaters  1,000 watt of Escorts Ltd @ Rs. 20

20 tube lights @ Rs. 8

7             Purchased stationery for cash Rs. 30

10            Bought of Bajaj & Co., on account:

30 Table lamps @ Rs. 25

10 Electric kettles @ Rs. 45

11            Purchased from Rama & Co., for cash

5 Immersion heaters 1,000 watt @ Rs. 19

12             Returned goods to Bajaj & Co.,

4 Table lamps

2 Electric kettles

15            Sales to Rahim on account

1 Immersion heaters,1000 watt @ Rs.25

1. Ascertain operating profit before working capital changes from the following details:

Rs.

Net profit before Tax and extraordinary items                                         2,00,000

Dividend received on long term investment in shares                                 40,000

Interest received on long term debentures of other companies                   30,000

Goodwill written off                                                                                   20,000

Discount on issue of shares written off                                                       10,000

Preliminary expenses written off                                                                 25,000

Depreciation charged on Fixed Assets                                                        65,000

Profit on Sale of equipment                                                                         10,000

Loss on Sale of Long term investments                                                         8,000

1. Prepare a Two – column Cash book from the following transactions of Ratan:

Jan 2007                                                                                           Rs.

1          Cash in hand                                                               40,000

6          Cash purchases                                                            20,000

12        Wages paid                                                                   1,000

15        Cash received from Suresh                                         60,000

Allowed him discount                                                              1,000

20        Cash paid to Rajesh                                                    25,000

21        Sold goods for cash                                                    25,000

25        Purchased goods from Shyam                                                12,000

22        Withdrew cash for personal use                                    5,000

1. Journalise the following transactions:

2008

Jan 1    Mr. Kumar commenced business with cash Rs.50,000,

Building Rs. 1,00,000, bank balance of Rs. 1,00,000

3    Purchased goods for cash Rs.7,000

5    Purchased goods for Rs.7,500 from Dinesh

7    Sold goods for cash Rs. 2,000

8    Paid rent Rs. 3,000 to Mr. James, the landlord

10  Withdrew cash from bank for personal use Rs.2,500

12  Returned goods worth Rs. 500 to Dinesh

15   Paid Rs.6,800 in full settlement to Dinesh.

1. Discuss the merits and limitations of financial accounting.
2. What are the significant uses of Cash flow statement?
3. Differentiate between Trial balance and Balance Sheet.

SECTION C

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

1. The following are the balances extracted from the books of Mr. Hari as on 31-12-2008. Prepare Trading and Profit & Loss Account for the year ending 31-12-2008 and a Balance sheet as on that date:

Trial Balance as on 31-12-2008

Particulars                                  Rs.                    Particulars                              Rs.

Drawings                                       4,000               Capital                                     20,000

Cash in hand                                 1,700               Sales                                        16,000

Cash at bank                                 6,500               Sundry Creditors                      4,500

Wages                                           1,000

Purchases                                      2,000

Stock (1-1-2008)                           6,000

Buildings                                     10,000

Sundry Debtors                             4,400

Bills Receivable                            2,900

Rent                                                 450

Commission                                     250

General expenses                             800

Furniture                                          500

40,500                                                               40,500

• Stock on 31-12-08 was Rs.4,000
• Interest on capital at 6% to be provided
• Interest on drawings at 5% to be provided
• Wages yet to be paid Rs.100
• Rent prepaid Rs. 50

1. From the following information make out a balance sheet with as many details as possible:

(a)  Gross profit turnover ratio                        25%

(b)  Debtor’s velocity                                      3 months

( c) Creditor’s velocity                                    2 months

(d)  Stock velocity                                          8 times

(e)  Capital turnover ratio                                2.5 times

(f ) Fixed assets turnover ratio                        8 times(on cost of sales)

Gross profit for the year ended 31st December 2008 was Rs. 80,000.  There was no long term loan or overdraft.  Reserves and surplus amounted to Rs. 28,000.  Liquid assets were Rs. 97,333.  Closing stock of the year was Rs. 2,000 more than the opening stock.  Bills receivable and Bills payable were Rs. 5,000 and Rs. 2,000 respectively.

1. From the following Receipts and Payments account for the year 31st December 2008 and the subjoined information, prepare the income and expenditure for the year ended 31-12-2008 and Balance Sheet as at 31-12-2008

Receipts and Payments Accounts

2008                                                          2008

Jan  1   To Balance b/d                               Dec 31 By Govt securities                 2,000

Cash in hand                    300            By Rent                                       300

Cash at bank                  3,000            By Furniture                                500

Dec 31 To  Subscription:                                     By Postage, printing                     50

2007         100                                     By Newspapers&

2008       2,000                                          Periodicals                                                                     2009                    50               2,150                                      2008     300

To Donations                      4,000                                      2009       60       360

To interest on investments     200            By Annual dinner                       800

(book value Rs.2,000)                        By Electricity charges

To collection for annual                                                   2007          60

Dinner                1,000                                    2008        330      390

To Sale of old Newspaper                       By balance b/d

Periodicals                           30                 Cash in hand               350

Cash at bank            5,930

6,280

10,680                                                           10,680

The club had furniture Rs. 5,000 on 1.1.2008.  Subscription outstanding for 2008 Rs. 200.  Rent Rs. 60 and Electricity charges Rs.30 were also outstanding for the year 2008.  Donations to be capitalized.

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## Loyola College B.Sc. Statistics April 2009 Estimation Theory Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

 YB 24

FIFTH SEMESTER – April 2009

# ST 5500 – ESTIMATION THEORY

Date & Time: 16/04/2009 / 9:00 – 12:00      Dept. No.                                                Max. : 100 Marks

PART A                                Answer all the questions                             [10×2=20]

1. Define the efficiency of an unbiased estimator. Give an example of a most

efficient estimator.

1. State the invariance property of consistent estimators..
2. State Factorization Theorem on sufficient statistic.
3. Show that exponential distribution with parameter λ is complete.
4. List out any two small sample properties of ML estimator.
5. Find ML estimator of θ in random sampling of size n from a population whose

pdf is  f(x, θ)   =          e – (x – θ),  for x > θ

=   0                      otherwise.

1. Define Loss Function. Is it a random variable? Justify.
2. When do we say that a statistic is Bayesian sufficient? Give an example.

9          Write down the normal equations of a simple linear regression model.

1. Mention the uses of Gauss-Markoff Model.

PART B                                            Answer any FIVE questions                       [5×8=40]

1. Show that the sample variance is a consistence estimator of the population

variance.

1. If X follows Binomial distribution with parameters n and p. Examine the

asymptotic unbiasedness of   T =    .

1. States and Prove Rao Blackwell Theorem.
2. Let (X1, X2, X3, …Xn) is a random sample from Poisson population with parameter

λ. Use Lehman Scheffe Theorem to obtain a UMVUE of λ

1. Obtain the moment estimators of the parameters of a two-parameter gamma

distribution.

1. Illustrate the invariance property of ML estimator through an example
2. Explain the method of modified Chi-square estimation.
3. State and prove Gauss Markoff model on BLUE

PART C                                            Answer any TWO questions                       [2×20=40]

1. (a) State and prove Cramer Rao inequality in one parameter regular case. When

does the equality hold good?

(b) Establish a sufficient condition for a biased estimator to become a consistent

estimator.

1. (a) State and prove Lehman Scheffe theorem on UMVUE

(b) Obtain a joint sufficient statistic of the parameters of the bi-variate normal

population.

1. (a) Derive the moment estimators of the parameters of two parameter uniform

distribution.

(b)            Derive the ML estimators of the parameters of normal distribution by solving

simultaneous equations.

1. (a) Establish a necessary and sufficient condition for a linear parametric function to

be estimable.

(b) Let (X1, X2, X3, …Xn) is a random sample of size n from Bernoulli population.

Obtain the Bayesian estimator of the parameter by taking a suitable prior

distribution..

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## Loyola College B.Sc. Statistics April 2009 Estimation Theory Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

 YB 25

FIFTH SEMESTER – April 2009

# ST 5501 – TESTING OF HYPOTHESIS

Date & Time: 17/04/2009 / 9:00 – 12:00       Dept. No.                                                       Max. : 100 Marks

SECTION – A

Answer ALL questions.                                                                              10 X 2 = 20

1. Define Best Critical Region.
2. What is power of a test?
3. Define Monotone Likelihood Ratio property.
4. Define a UMP level α test.
5. Describe the stopping rule in SPRT.
6. State any two properties of likelihood ratio tests.
7. Write the 95 % confidence interval for population proportion based on a random sample of size n. (n > 30)
8. Describe the assumptions of t – test for testing equality of means of two independent
9. State any two assumptions of non-parametric tests.
10. Describe a test based on F- distribution.

SECTION – B

Answer Any FIVE questions.                                                                                       5 X 8 = 40

1. Let X have a Poisson distribution with λ {2, 4 }. To test the null

hypothesis H0: λ = 2 against the alternative simple hypothesis H1: λ = 4, let the

critical region be {X1  X1 ≤ 3}, where X1 is the random sample of size one. Find

the power of the test.

1. Based on a random sample of size n (n   30), construct a 95 % confidence interval for the population mean.

1. If  is a random sample from B (1, ),   (,1 ) , derive the

uniformly most powerful test for testing H0:  =  against H1:  >

1. Let be a random sample from Binomial distribution with parameter. Show that the distribution has a monotone likelihood ratio in the statistic Y =

1. Describe the procedure of Sequential Probability Ratio Test.

1. Based on a random sample of size n from B(, 0 <  , derive the SPRT

for testing H0:  against the alternative  hypothesis H1:  at level =0.05.

1. Differentiate parametric and Non-Parametric testing procedures.

1. Explain Kolmogorov- Smirnov one sample test.

SECTION – C

Answer any TWO questions.                                                                    2 X 20 = 40

1. a. State and prove Neyman-Pearson theorem.       

1. Based on a random sample of size n from a distribution with pdf

f(x, ) =        0 < x < 1

• otherwise

find the best critical region for testing null hypothesis H0: = 2 against the

alternative simple hypothesis H1:  = 3.                                                         

1. Based on a random sample of size n from U(0,θ), derive the likelihood ratio test

for testing  H0:  against the alternative hypothesis H1:  .

1. a. Describe the procedure of testing H0 : based on a random sample of

size n, using Wilcoxon’s statistic.                                                                    

1. In SPRT, under standard notations prove that and

1. Explain: i) Sign test for location                          ii) Level of significance

iii) Test of equality of two variances      iv) Randomized test.      [ 4 x 5 ]

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## Loyola College B.Sc. Statistics April 2009 Econometric Methods Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

 YB 31

FIFTH SEMESTER – April 2009

# ST 5405 – ECONOMETRIC METHODS

Date & Time: 30/04/2009 / 1:00 – 4:00  Dept. No.                                                    Max. : 100 Marks

SECTION A

Answer all questions                                                                         (10 x 2 = 20)

1. What is the difference between a ‘Mathematical model’ and an ‘Econometric model’?
2. Define Sample Regression Function.
3. Mention any two properties of OLS estimators.
4. What is meant by ‘Time series’ data? Give an example for the same.
5. Interpret the following regression equation.

Y = 2.5 + 0.21X1 + 1.0X2 ,

where Y denotes the weekly sales( in ‘000’s)

X2 denotes the number of sales persons.

1. In a multiple regression model, the value of R2 is found to be 0.657. How is it interpreted?
2. For a two variable regression model, the observed and estimated (under OLS) values of Y are given below:

Observed Y:   10         14        13        12        17

Estimated Y:  10         13        11        14        15

Calculate the standard error of the regression.

1. What is meant by ‘dummy variable’?
2. Mention any two methods of overcoming multicollinearity.
3. Define Heteroscedasticity.

SECTION B

Answer any five questions                                                                (5 x 8 = 40)

1. Explain the various steps involved in an Econometric study.
2. Explain the method of least squares and hence obtain the OLS estimators for the intercept and slope parameters based on a two variable linear model.
3. The following data relates to the family income(X) and expenditure(Y) (both in dollars per week) of 8 families randomly selected from a small urban population.

Y: 40   55   50   70   80   100  90  78

X: 60   65   70   63  120  75    68  52

Assuming there is a linear relationship between Y and X, perform a regression of Y on X and estimate the regression coefficient. Also find an unbiased estimate for the variance of the disturbance term.

1. Consider the following information from a 4 variable regression equation:

Residual sum of squares = 94;

Y = 10,12,14,9,7,8,2,22,4,12.

a.) Find TSS and ESS.

b.) Test the hypothesis that R2 = 0 at 5% level.

1. Explain the procedure of obtaining a 100(1-α) % confidence interval for the slope parameter in a two variable linear model.
2. What is meant by ‘structural change’? Explain the Chow test for detecting structural change in a ‘k’ variable model.

1. What is meant by dummy variable trap? Explain the methods to overcome it.
2. Consider the following data set:

Sample no.:     1           2          3          4          5

Y:    15         10        14        8          3

X:    1           2          3          4          5

Calculate the standard errors of the intercept and slope coefficients if their OLS

estimates are 17.8 and -2.6 respectively.

SECTION C

Answer any two questions                                                                (2 x 20 = 40)

1. a.) For a two variable linear model, show that the least squares estimators are
unbiased.

b.) Mention the various assumptions in a Classical Linear Regression model.

(10 + 10)

1. Consider the following data on annual income (Y) (in 000’s \$), total
experience (X1) and age (X2).

Y: 12        10                    14      15       6      11       17

X1: 8          7          9       10       4       6.5      12

X2: 32        29        35     33       26     28       39

Perform a regression of Y on X1 and X2. Interpret the results. Also test the
hypothesis that all the slope parameters are significantly different from zero at

5% level by constructing the ANOVA table.

1. a.) Consider the following ANOVA table based on an OLS regression

 Source of Variation Degrees of Freedom Sum of Squares Regression ? 1000 Error 35 ? Total 39 2200

1. i)  How many observations are there in the sample?
2. ii) How many independent variables are used in the regression?

iii) Find the missing values in the above table

1. iv) What is the standard error of regression?
2. v) Calculate the value of R2
3. vi) Test the hypothesis Ho : R2 = 0 vs H1 : R2 ≠ 0 at  5% level.

b.) What is meant by multicollinearity? Explain its consequences.  (12+8)

1. a) Explain the method of generalized least squares to obtain the estimators of

a linear model in the presence of heteroscedasticity.

b.) Write short notes on:

1.) Disturbance term in a linear model.

2.) Differences between correlation and regression.

3.) Differential intercept coefficient.

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## Loyola College B.Sc. Statistics April 2009 Distribution Theory Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

 YB 19

B.Sc. DEGREE EXAMINATION – STATISTICS

FOURTH SEMESTER – April 2009

# ST 4501 – DISTRIBUTION THEORY

Date & Time: 24/04/2009 / 9:00 – 12:00        Dept. No.                                                       Max. : 100 Marks

PART – A

Answer ALL Questions                                                                                                   (10 x 2 =20)

1. Show that the function  is a probability density function.
2. Define : Conditional Variance with reference to a bivariate distribution.
3. Write the density function of discrete uniform distribution and obtain its mean.
4. Find the mean of binomial distribution using its moment generating function.
5. Find the maximum value of normal distribution with mean and variance.
6. Write down the density function of bivariate normal distribution.
7. Define : t Statistic.
8. Find the density function of the random variable where is the distribution function of the continuous random variable .
9. State central limit theorem for iid random variables.
10. Obtain the density function of first order statistic in.

PART – B

Answer any FIVE Questions                                                                                         (5 x 8 =40)

1. Let be iid RVs with common PDF . Write . Show that and are pairwise independent but not independent.
2. Let be independent RVs with common density given by

Find the distribution of .

1. Derive the characteristic function of Poisson distribution. Using the same find the first three central moments of Poisson distribution
2. Establish the lack of memory property of geometric distribution
3. Obtain the marginal distribution of X if (X,Y) follows bivariate normal distribution
4. Obtain the moment generating function of chi-square distribution and hence establish its additive property
5. Show that if , then
6. Derive the formula for the density function of rth order statistic

PART –  C

Answer any TWO Questions                                                                              (2 x 20 =40)

1. Let (X,Y) be jointly distributed with density

Find

1. (a) Obtain the moment generating function of Normal distribution and hence find its

mean and variance

(b) Show that, if X and Y are independent poisson variates with parameters and

,  then the conditional distribution of X given X+Y is binomial.

1. Derive the density function of t distribution and obtain its mean.

1. Write descriptive notes on the following :
• Stochastic independence
• Multinomial distribution
• Transformation of variables
• Stochastic Convergence

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## Loyola College B.Sc. Statistics April 2009 Design & Analysis Of Experiments Question Paper PDF Download

 YB 28

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

SIXTH SEMESTER – April 2009

# ST 6600 – DESIGN & ANALYSIS OF EXPERIMENTS

Date & Time: 18/04/2009 / 9:00 – 12:00             Dept. No.                                                   Max. : 100 Marks

PART – A

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

1. Give a contrast orthogonal to the contrast
2. What is a mixed effect model?
3. Mention the principle of experimental design which is not taken care by CRD if fertility gradient is present in one direction
4. Give the skeleton ANOVA table for two-way classification with interaction
5. What should be the number of treatments if the error degrees of freedom associated with a Randomised Block Design with 5 blocks is 12?
6. What are Latin Squares ? Give an example of a latin square.
7. Write all possible treatment combinations in a design.
8. When do you recommend confounding ?
9. Write the factorial effect corresponding to in design
10. If the interactions BCD and ABE are confounded in a replication consisting of four blocks of 8 plots in factorial design which effect also gets confounded automatically.

PART – B

Answer any FIVE Questions.                                                                            (5 X 8 = 40 marks)

1. Explain in detail the principles of experimental design.
2. Write a descriptive note which highlights the difference between fixed effect and random effect models.
3. Develop ANOVA for one way classified data
4. Derive the formula for estimating the missing value in a LSD when one observation is missing.
5. Explain the preparation of layout of a 5 x 5 Latin square design.
6. Explain the process of computing various factorial effects in the case of a design.
7. Illustrate with an example the method of finding the contrast defining the interaction between a Quadratic Effect and Linear Effect in the case of a factorial design involving two factors with three levels each.
8. It is decided to confound an effect in the case of a experimental design.
• What will be your choice of the effect to be considered for confounding ? Justify your answer.
• Explain the preparation of lay out for such a confounding in 4 replications.

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. Develop the complete analysis of Balanced Incomplete Block Design
4. Write short notes on the following:
• Efficiency of RBD over CRD b) Cochran’s theorem   c) Generalized Effect

(d) Partial Confounding

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## Loyola College B.Sc. Statistics April 2009 Computational Statistics Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

 YB 27

FIFTH SEMESTER – April 2009

# ST 5503 – COMPUTATIONAL STATISTICS

Date & Time: 04/05/2009 / 1:00 – 4:00       Dept. No.                                          Max. : 100 Marks

Answer any THREE questions. Each carries 34 marks.

1. 1. (i) Find seasonal variations by ratio-to-trend method from the data given below:
 Year 1st Quarter 2nd Quarter 3rd Quarter 4th Quarter 1999 30 40 36 34 2000 34 52 50 44 2001 40 58 54 48 2002 54 76 68 62 2003 80 92 86 82

(ii) Assuming a four yearly cycle, calculate the trend by the method of moving averages from the following data relating to production of tea:

 Year 1961 ‘62 ‘63 ‘64 ‘65 ‘66 ‘67 ‘68 ‘69 ‘70 Production 464 515 518 467 502 540 557 571 586 612

1. In a population with N = 4, the Yi values are 1, 2, 3, 4. Enlist all possible samples of size n = 2, with SRSWOR and verify that E (s2) = S2.

1. 3. (i) A sample of 30 students is to be drawn from a population consisting of 300 students belonging to two colleges A and B. The means and standard deviations of their marks are given below:
 Total no. of students(Ni) Mean Standard deviation(σi) College A 200 30 10 College B 100 60 40

How would you draw the sample using proportional allocation technique? Hence obtain the variance of estimate of the population mean and compare its efficiency with simple random sampling without replacement.

(ii) An institution which gives coaching for students planning to appear for a competitive exam in English wishes to test the efficacy of its coaching programme in improving this course. Then pre-coaching and post-coaching tests are conducted. The following data were obtained from a sample of 15 students who were subjected to both the tests:

Pre-coaching score: 56, 47, 61, 79, 53, 68, 72, 85, 59, 61, 70, 53, 68, 77, 83

Post- coaching score: 97, 53, 63, 82, 53, 64, 83, 89, 66, 63, 70, 50, 60, 84, 89

Carry out the relevant tests and report your findings.

1. (i) Calculate Laspeyre’s, Paasche’s, Bowley’s and Fisher’s Ideal index from the following data.

 Commodity Price (2004) Value (2004) Price (2005) Value (2005) Bricks 10 100 8 96 Sand 16 96 14 98 Timber 12 36 10 40 Cement 15 60 5 25

(ii) Calculate chain based index numbers from the price of the following three commodities:

 Commodity 1999 2000 2001 2002 2003 Wheat 4 6 8 10 12 Rice 16 20 24 30 36 Sugar 8 10 16 20 24

1. (i) Suppose that a group of 100 men received a flu vaccine and five of them died within the next one year. It is known that the probability of a man who did receive the vaccine will die within the next year is 0.02. Given this information, is the above mentioned event unusual or can this death rate be expected normally?

(ii) A new drug is to be tested for the treatment of patients with unstable angina. The effect of this drug is unknown. The following changes in the heart rate were observed among 20 patients: 4, -2, -3, 8, -3, -4, 2, 0, 1, 6,   -4, -7, 3, -3, 0, 5, 6, 3, -4, -2. The experimenter would like to know whether the drug induces a significant change in heart rate after 48 hours of administration.

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## Loyola College B.Sc. Statistics April 2009 C And C ++ Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

 YB 21

FIFTH SEMESTER – April 2009

# ST 5401 – C AND C ++

Date & Time: 30/04/2009 / 1:00 – 4:00 Dept. No.                                                    Max. : 100 Marks

SECTION A

Answer all questions.                                                                           (10 x 2 = 20)

1. Mention any four special operators available in C language.
2. What is the use of getchar function?
3. If y = 18, what is the value of y << 1?
4. What is meant by nested loop? Give an example.
5. Write a C program to find the area of a circle with radius ‘r’.
6. Mention any four keywords available in C++ but not available in C.
7. What is meant by polymorphism?
8. Give the syntax of cin and cout statements.
9. Write a C++ program to find the greatest among 2 integers.
10. If int a[] = {12,3,0,1,2}, what is the value of a – a + a?

SECTION B

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

1. Explain the various input and output functions available in C language.
2. Write a C program to display all the prime numbers between 1 and 100.
3. Explain any two types of ‘if’ statements available in C and give an example for each.
4. Write a C program to accept ‘n’ integers and display them in ascending order.
5. What is meant by object oriented programming? Explain its advantages.
6. Write a C++ program that makes use of the concept of friend function.
7. Write short note on recursive functions and give an example.
8. Write a C++ program to accept ‘n’ integers and display their mean and variance.

SECTION C

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

1. a.) Explain the syntax of do – while statement and give an example.

b.) Write a C program to accept a matrix of order m x n and display

its transpose.                                                                                  (10+10)

1. a.) Write a C program to accept an alphabet and display whether it is a vowel
or a consonant.

b.) Create a structure by name ‘employee’ that contains the following data    members: employee id, basic salary for 10 employees. Write a program to accept the employee id and basic salary for the10 employees by making use of the above structure and display their total income which is the sum of basic salary, DA and HRA where DA is 60% of basic salary and HRA is 20% of basic salary.                                                                                           (8+12)

1. a.) Explain the different access specifiers available in C++ with examples.

b.) Write a C++ program to overload the operator ‘+’.                       (10+10)

1. a.) Write short notes on structures and arrays.

b.) Write a C++ program that makes use of the concept of simple inheritance.                                                                                                                                 (10+10)

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## Loyola College B.Sc. Statistics April 2009 Basic Sampling Theory Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

 YB 13

THIRD SEMESTER – April 2009

# ST 3502 / ST 4500 – BASIC SAMPLING THEORY

Date & Time: 02/05/2009 / 9:00 – 12:00   Dept. No.                                                   Max. : 100 Marks

PART A (10 x 2 = 20 Marks)

1. Distinguish between census method and sampling procedure.
2. Define Sampling design and Probability Sampling.
3. What is simple random sampling?
4. Prove that SRSWOR sample mean is an unbiased estimate of the population mean.
5. Write down the two steps to select one unit by Lahiri’s method of PPS selection.
6. What is PPSWR sample?
7. Explain the need of stratified sampling.
8. What is proportional allocation?
9. What is circular systematic sampling?
10. What is a balanced systematic sampling scheme?

PART B (5 x 8 = 40 Marks)

1. What are the advantages of sampling over census method? What are its limitations?
2. Under simple random sampling is unbiased for the population total and also obtain its variance.
3. Marks secured by over one lakh students in a competitive examination were displayed jin 39 display boards. In each board marks of approximately 3000 students were given. Kiran, a student who scored 94.86 marks wanted to know how many candidates have scored more than him. In order to estimate the number of student who have scored more than him, he took a SRS of 10 boards and counted the number of students in each board who have scored more than him. The following is the data collected.

14, 29, 7, 13, 0, 36, 11, 43, 27 and 5.

Estimate the number of student who would have scored more than Kiran and also estimate the variance of its estimate.

1. Prove that the probability of selecting the ith unit in the first effective draw is , in Lahiri’s method of  PPS selection.
2. Derive the variance for Hansen – Hurwitz estimator.
3. Explain the procedure of optimum allocation of sample size.
4. Derive an unbiased estimator for the population total and its variance under proportional allocation.
5. Prove that , where  and  are the conventional expansion estimators under linear systematic sampling and simple random sampling respectively.

PART C (2 x 20 = 40 Marks)

1. (a) Prove that under SRS, Sxy.

(b) Derive average mean squared errors under balanced systematic and modified systematic sampling schemes and compare them.

1. (a) Derive an unbiased estimator for population total in PPS sample and also obtain its variance.

(b) Prove that in Stratified random sampling with given cost function of the form , is minimum if .

1. If the population consists of a linear trend, then prove that .
2. (a) Obtain the relative efficiency of systematic sample as compared to simple random sampling without replacement.

(b) Describe Lahiri’s method of selection and its merits over cumulative method.

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## Loyola College B.Sc. Statistics April 2009 Applied Stochastic Processes Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

 YB 20

FIFTH SEMESTER – April 2009

# ST 5400 – APPLIED STOCHASTIC PROCESSES

Date & Time: 28/04/2009 / 1:00 – 4:00  Dept. No.                                                   Max. : 100 Marks

SECTION – A

Answer all the questions                                                                                             (10 x 2 = 20 )

1. Define Stochastic Process with an example.
2. What is the State Space of a Stochastic Process?
3. Define Markov Process.
4. Explain Independent Increments.
5. Define Transition Probability Matrix.
6. If P = is a Stochastic Matrix, fill up the missing entries in the Matrix.
7. Define Accessibility of a State from another state.
8. What is a Recurrent State?
9. Define aperiodic Markov Chain.
10. What is a Martingale?

SECTION – B

Answer any Five questions                                                                                          (5 x 8 = 40)

1. State the classification of Stochastic Processes based on time and state Space. Give an example for each type.
2. Describe One-dimensional Random Walk and write down its Transition Probability Matrix.
1. Let { Xn, n ³ 0} be a Markov chain with three states 0,1,2 and with transition

probability matrix

and the initial distribution Pr{ X0 = i}= 1/3, i = 0,1,2

Find    i)   Pr{X1 = 1 ½ X0 = 2},                          ii)   Pr{X2 = 2 ½ X1 = 1}

iii)   Pr{X2 = 2, X1 = 1 ½ X0 = 2},     iv)   Pr{X2 = 2, X1 = 1, X0 = 2}

1. Show that Communication is an equivalence relation.
2. Consider the following Transition Probability Matrix.  Using the necessary and sufficient condition for recurrence, examine the nature of all the three states.
3. State any one property of Poisson Process.

1. Classify the states of Markov Chain with Transition Probability Matrix

1. State and stablish Chapman – Kolmogorov equations for a discrete time Markov chain.

SECTION – C

Answer any Two questions                                                                                       (2 x 20 = 40)

1. Derive the distribution of X(t), is a Poisson Process.                               (20)
2. a). State and prove a necessary and sufficient condition for a state to be Recurrent .

b). Explain the Two-dimensional Symmetric Random Walk.                                   (10+10)

1. (a) Let { Zi, i = 1,2…} be a sequence of independent identically distributed random variables   with mean 1.  Show that   Xn =   is a Martingale                                             (8)

(b). Consider a Markov Chain with Transition Probability Matrix

Find the equivalence classes and compute the periodicities of all the four states.           (12)

1. a). Illustrate with an example Basic Limit Theorem of Markov chains..

b). Consider the following Transition Probability Matrix explaining seasonal changes on

successive day. (S – Sunny, C – Cloudy)

Today state

yesterday state

Compute the stationary probabilities and interpret the results.                            [10+10]

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## Loyola College B.Sc. Statistics April 2009 Actuarial Statistics Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

 YB 23

FIFTH SEMESTER – April 2009

# ST 5404 – ACTUARIAL STATISTICS

Date & Time: 28/04/2009 / 1:00 – 4:00       Dept. No.                                                       Max. : 100 Marks

PART – A

ANSWER ALL THE QUESTIONS                                                             (10  x 2 = 20)

1. Find the present value of Rs. 1000 receivable at the end of 50 years the rate of interest being 5% p.a.
2. Write the formula for finding effective rate of interest given the nominal rate of interest.
3. Write the two relations between  and .
4. Define the two types of perpetuity.
5. Explain  , .
6. Define and .
7. Explain life annuity, temporary life annuity.
8. Explain the principle of life insurance.
9. Explain the pure endowment assurance.

PART – B

ANSWER ANY FIVE QUESTIONS                                                             (5 x 8 = 40)

1. Two loans of Rs.500 each are made out to A three years ago and 2 years ago respectively and an interest of 6% p.a. was agreed upon.  At present A could make a repayment of Rs. 400.  He promises to clear the dues at the end of 2 years from now.  How much will he have to pay then?
2. Derive the formula for  and .
3. A has taken a loan of Rs.10,000.  He pays the level annual payment at the end of each year for 5 years.  What is the installment amount? What is the amount towards the principle in the third payment?  What is the principal outstanding at the end of 3 years?
4. Find the accumulated value of an annuity due of Rs. 400 p.a. payable in equal quarterly installments for 12 years certain at nominal rate of interest of 7% p.a. convertible half yearly.
5. Find the probability that
• a life aged 35 will die between 45 and 50
• a life aged 35 will die after 60
• a life aged 35 will die in the 10th year from now.
• A life aged 35 will survive another 10 years.
1. On the basis of LIC table at 6% calculate the net annual premium ceasing after 15 years or at previous death for money back policy on (45) to secure the following benefits.
• 1500 on survivance to the end of 5 years.
• 1500 on survivance to the end of 10 years
• 3000 on survivance to the end of 15 years
• 6000 on death at any time within 15 years
1. Derive the formula for present value when the successive instalments form an arithmetic progression.
2. Explain the various types of life annuities.

PART – C

ANSWER ANY TWO QUESTIONS                                                           (2 x 20 = 40)

1. a). Payments of (i) Rs 50 at the end of each half-year for the first 5 years followed by (ii). Rs 50 at the end of each quarter for the next 5 years, are made into an account to which interest is credited at the rate of 9% p.a. convertible half-yearly.  Find the accumulated value at the end of 10 years.

b). Provident fund (PF) deductions are made at the rate of Rs. 200 per month.                   Find the accumulated value at the end of 10 years, at a rate of interest 10% p.a.

( 10 + 10)

1. a). Derive the formula for ,

b). A special policy provides for the following benefits.

(i). An initial sum of Rs. 10,000 with guaranteed annual additions of Rs.250                            for each years premium paid after the first if death occurs within the term                                   of assurance .

(ii). Rs 10,000 payable on survivance to the end of the term of assurance and

(iii). Free paid up assurance of Rs.10,000 payable at death after expiry of the                               term of assurance.  Calculate net annual premium under the policy on the                        life of (35) for 25 years.                                                    ( 10 + 10)

1. a). Complete the following life table
 Age 35 86137 742 .00842 36 – – .00885 37 – – – 38 – – – 39 – – .00969

b). Three persons are aged 30,35,40 respectively.  Find the probability that

(i). One of them dies before 45 while the others survive to age 55.

(ii). Atleast one of them attains age 65.

(iii). All of them die after 70.

(iv). None of them reach age 70.

(v). exactly 2 of them die before 45 and one survive to age 60.    ( 10 + 10)

1. Write short notes on any three of the following

(i). Children deferred assurances  (ii). Double endowment assurances.

(iii). Equation of value                  (iv).  and

(v). Present value of perpetuities.                                         ( 10 + 10)

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## Loyola College B.Sc. Statistics Nov 2009 Database Management Systems Question Paper PDF Download Go To Main page

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