Time Allowed: 3 Hours Maximum Marks: 300
Caniliilates shouldaJtempt Questions 1 and 5 which arecompulsory, andanythreeoftheremaining
questions selecting oJ least one questionfrom e(f£h Section.
Assume suitahle data ifconsiderednecessary andindicntethe sameclearly.



SECTION A
Attempt any five sub-parts of the followmg

Explain the construction of X(bar) and r-charts Why are both the charts used simultaneously?

Explain the construction and use of sequentia1 sampling plans for attributes

Explain the difference between Reliability, Maintain-ability, and Availability illustrate your answer by suitable examples

Describe the M-technique with artificial variables to minimize objective function in a linear programming problem. What changes will be made in the procedure if the objective function is to be maximized?

Describe MICII and GI|M|l queues. Derive the Pollaczek-Khinchin mean value formula for the average number of customers in queue.

If states i and j of a Markov chain communicate with each other, then show that if state i is recurrent then state j is also recurrent.

2
Explain the construction and use of cumulative sum chart.

Find the reliability function and failure rate function for the lognormal time-to failure distribution

Explain different types of censoring in life testing experiments. When are these used?

3
Stale and prove duality theorem in linear programming.

Show that, for a Markov cham, if state j is persistent non-null, then as n
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Discuss some statistical problems which can be solved by using well known Statistical Software Packages like SPSS and which otherwise are difficult to solve.

4
Distinguish between multiple and sequential sampling plans. Derive the OC function and ASN of a double sampling plan under corrective sampling scheme.

Let denote the failure time distribution of the ith component in a series system consisting of n independent components. Find the system failure time density.

Determine the optimal ordering policy in the case of a single period inventory model with no set up cost, instantaneous stock replenishment and the amount demanded is a continuous random variable

What is sensitivity analysis? Explain its use with the help of an example



SEcnON B

Attempt any five sub-parts of the followmg

What are the salient features of the Box-Jenkins approach to time series forecasting?

What are the advantages of a chain ,index over a fixed base index number?

What are the official agencies responsible for the collection of data on

population,
agriculture,
trade, and
prices?

Distinguish between complete and abridged life tables

Define complete expectation of life and curtain expectation of life Show that
Also comment on the nature of as a function of x

What is path analysis? Explain its use in psychometrically.

6
What are the different methods for determining seasonal variations in a time series? Indicate the seasonal patterns to which these methods are applicable
Describe the essential steps for the construction of an index number of agriculture production

Discuss the advantages and limitations of two-stage least squares method of estimation.

7
Define Crude Death Rate and Standardized Death Rate (STDR) Discuss which one of these two rates can be used to compare the mortality situations of two different places
Define a logistic curve and examine its suitability as Method of fit a logistic curve as a growth model. Describe Rhodes's Method of fit a logistic curve.
What are morbidity incidence rate and morbidity prevalence rate? How are they computed? Explain their uses.

8
Describe the methods of collection of official statistics on agriculture production and prices What are their limitations and reliability?
Explain the functions of CSO as part or the present statistical system in India.
Define T-scores computed and percentile scores. Describe why they are used and how these are computed.
What is reliability coefficient of a test? Describe some practical methods of estimating test reliability