CS (MAIN) EXAM, 2010 STATISTICS Paper II
lri111e Allo1ved Three Hours I Marks 300J:
INSTRUCTIONS
Each question is printed bot/J in Hindi and in
English.
Answers must be written in tfte 1nediun1 specified i11
the Ad,nission Certificate issued to you, which
niusl be stated clearly on the cover of the answerbook
in the space provided for the purpose. No
marks will be given for the answers written in a
mediun1 other thail that specified in the Ad1nission
Ce rtifi.cate.
Candidates should atte1npt Question Nos. 1 and 5
1vhich are co,npulsory. and any three of the
re,naining questions selecting at least one question
fr oni each Section.
Assunie suitable data if considered necessary and
indicate the san,e clearly.
Sy,nbolslnotations used carry usual meaning??
unless othenvise indicated.
Charts/figures, wherever required, are to be drawn
in the an.nver book itself and not on separate graph
sheet.
The n??unber of marks carried by each question is
indicated at the end of the question.

Section
1. Attempt any five of the following: 12x5=60
if i is a recurrent state with period t with a given mean recurrence time newii.then show that<br><br> <img src='./qimages/908-1a.jpg'>
In queuing mode1, obtain the expression for the probability that there are n units in the system at any time. . .
What js rectifying inspectio?? plan? Obtain the expressions for AOQ and ATi t with reference to a single sampling plan for attributes.
Solve graphically the following linear programming problem
Min 3x 1 5x2
subject to -3x 1 4x2<=12
2x1-x2
2x 1 3x2 12
X1 X2
x X2 0 ..
·Explain fixed order quantity approach and periodic review approach in Inventory control.
Explain the replacement policy for item whose running cost increases with tit:ne but value of money changes with constant rate during the period??

2. Explain assignment problem and transporta- tion problem. Give its mathematical formulation. 10
At time· zero, all items in a system are new. each item has a . probability p of failing immediately before the end of the first month of life, and: a probability q 1 of failing immediately. before the end of the second month (i.e., all frems fail by the end of the second month). If all items are replaced as they fail, then show that the expected number of failures at the end of month xis given by N where N is the number of items in the system. . . 20
State and prove Fundamental theorem of game theory. 10
Suppose there is a product of brands A and B respectively. Let each of these two brands have • • exactly 50 per cent of the total market in same period and let the market be of a fixed size. The transition matrix is given below <img src='./qimages/908-2d.jpg'> If the initial market share breakdown· is 50% for each brand, then determine their market shares in the steady-state. 20

3. For any zero-sum two-persons game where the optimal strategies are not pure strategies and for which pay off matrix is <img src='./qimages/908-3a.jpg'> 25
A repairman is to be hired to repair machines that breakdown following a Poisson process with an average rate of four per hour. The cost of non-productive machine is Rs. 90 per hour .. The company has the option of choosing either a fast repairman who charges Rs. 60 per hour and repairs machines at the rate of 7 per hour or slow repairman who charge:s Rs .. 30 per hour and repairs machines at the rate of 5 · per hour.. Taking the cost in to the consideration find which repairman should be hired. 20
An aircraft company uses rivets at a constant 'rate of 2500 per year. Each unit costs Rs. 30 and the company personnel estimate that it costs Rs. 1 30 to place an order?? and that the carrying · cost of inventory is 1 per year. How frequently should orders be placed Also determine the optimum size of each order. 15
4. A firm manufacturing a single product has three plants Y and Z. The three plants have produced 60. 35 and 40 units respectively during this month. The firm had made commitment to sell 22 units to customer A 45 units to customer .20 units to customer 1 8 units to customer D and 30 units to customer E. Determine the minimum possible transportation cost of shifting the manufactured products to the five customers. The net per unit cost · of transporting from the three plants to five customers is"given below <img src='./qimages/908-4a.jpg'> 25

The following data (pertaining to two subgroups of size · i s from two different machines which are supposed to be alike. Plot the necessary charts to show whether their product would support this assumption. If they do not support this assumption, does this prove the machines are not essentially alike <img src='./qimages/908-4b.jpg'> 20
Define Reliability. List out some of the problems in achieving reli abil ity. How you will distinguish between Reliability and quality control 1 5

Section

5. Answer any five of the following 12x5=60
What is identification problem Explain the rank and order conditions of identifiability.
Define Time series. Explain briefly different components of Time series.
Explain Q uasi Stable theory of Population .
Explain the concept of Auto covariance, Auto correl ation and their functions.Also explain how the fun ctions are estimated.
Define Index Number.What does an Index.Number me an? Explain the uses of Index Numbers .
Explain briefly the concept of path analysis. Mention their uses in Psychometry.

6. Expl ai n the conc ept of Val idi ty. How one cara esthnate the Va Hdi ty Expl ai n what are the different ty pes of validity Also di scuss the concept of test length with re spect to validi ty. 20
What are the fo ur important stages in ARIMA modelling of a times series data Explain briefly. 20
What is Heteroscedasticity Write its nature and consequences ." Describe the Speannan's rank correlation test useful for detecting Heterosc edasticity. 20

7. Show that Fisher's ideal inde x number and Marsa11 Edgeworth index number lie between Laspeyre's and Paasche's index numbers . 25
A given test has a reliability coefficient of 0.8 and standard deviation of 20.
What is the maximum correlation which this test i s ·capable of yielding as it stantls
What is the· S .E. of a score obtained on this test.
What is the estimated reliability coefficient of this test in a group in which standard deviation is 15
What proportion of the variance of the score s in thi s test is attributable to "true" variance 20
Expl ain different measures of mortality. Briefl y discuss about the procedure for finding standardization of rates through di rect and indi rect methods.15

8. What is Cost of living Index Mention the mai n steps in construction of the cost of living index leval ues. How you will construct it . Explain both the methods. . 25
Expl ain briefly the sy stem of collection of industrial stati stics in India. Also mention i ts reli ability and limitations. 20
With usual notation show that <img src='./qimages/908-8c.jpg'>
Note English version. of th e ln structio1is · is pri11 ted on th e fro nt cover of this question paper.