STATISTICS



Time Allowed: 3 Hours Maximum Marks: 300
Caniliilates shouldaJtempt Questions 1 and 5 which arecompulsory, andanythreeoftheremaining
questions selecting oJ least one question/rom e(f£h Section.
Assume suitahle data ifconsiderednecessary andinilicnte the same clearly.
Notations andsymbols used are as usual

SECTION A
Answer any five sub-parts of the following
1.(a)Distinugish between chance causes and assignable causes and (ii)specification limits and control limits.

What is a CUSUM chart and where is it used? How does it differ from a Shewhart control chart?

(c)Explain renewal density and renewal function.

(d)Show that the set of feasible solutions to a linear programming problem is convex.


(e)State the chief characteristics of a queuing process. For the queuing process FCFS/co), derive its steady state solution.
(f)For the Markov chain With transition probability matrix <img src='./qimages/1125-1f.jpg'>

2.(a)Describe a double sampling plan for attributes Derive the expressions for OC, ASN &ATI of this plan.

(b)Describe and illustrate the concepts of (i)reliability and maintainability.
given the hazard function lamdat(lamda>0),compute the reliability function the mean time to failure.

3.(a)Explain what you understand by an assignment problem Solve the following assignment problem for minimizing total time. <img src='./qimages/1125-3a.jpg'>


(b)Discuss the inventory problem when the demand lS stochastic having a discrete probability distribution

(c)Show that in an irreducible Markov chain, all the states are of the same type -these are all transient or all persistent null or all persistent non-null.
Explain clearly the basis and working of control chart for mean and range Given interpretation of X bar and R charts.

(b)What are SurviVal models? Explain bath-tub and Weibull Survival models.
(c)For the queuing model obtain (i)the mean queue length and the average number of units in the system
(d)Describe the use of SPSS software packages with an illustration.


SEcnON B
Attempt any five sub-parts of the folloWing
5.(a)What is a time series? Explain briefly the various components of a time series Also explain the additrve and multiplicative models.
(b)What are index numbers? Explain their uses. Discuss the difference between fixed-base and chained-base index numbers
(c)What are the principal publications relating to data on agricultural statistics, trades statistics and Joint-stock companies?

(d)Distinguish clearly between stable and stationary populations.
(e)Define total fertility rate,(ii) age-specific death rate and expectation of life.
(f)Define T-scores. Explain the method of computing T-scores from raw test scores.

6.(a)State the different methods for determining the seasonal variation in a time series Describe the Link-Relative method
(b)Describe the essential steps for the construction of a cost of living index number.
(c)Describe the method of two-stage least squares to estimate the parameters of a given equation in a system of Simultaneous equation; and show that these estimators are consistent.

7.(a)Define gross and net reproduction rates Explain the computation of net reproduction rates Interpret its value being less than, equal to or greater than unity.
(b)State the basic assumptions while constructing a life table. In the usual notations, show that
<img src='./qimages/1125-7b.jpg'> What is an abridged life table?

(c)State the main features of a logistic curve and explain its suitability as a growth model.How is this curie filled to observed data?
8.(a)Describe the present official statistical system in India relating to information about population.
(b)Describe the offic1al method adopted for collection and publication of economic data and indices in our country.

(c)What is meant by intelligence quotient Describe the procedure and tests for measuring IQ.

(d)Describe the following methods of determining the reliability of tea scores: (i)Split-half technique
(ii)Rational equivalence