C S MINS 2015 STATISTICS (PAPER-II)


l. Explain the term ‘control’ in connection with Statistical Quality Control. Distinguish between Process control and Product control.

Define Type I censoring, Type II censoring and Random censoring. Describe the situations in which they may arise, either by design or due to experimental circumstances,

In the context of a rectangular game, give the concepts of payoff matrix, pure strategy of players and mixed strategy of players.

For a FCFS) queue system, compute

expected number of customers in the system;

expected queue length;

expected (average) waiting time of a customer in the system.

Mention the importance of sensitivity analysis. What are the different problems that are resolved through it?


2. State the single sampling plan for attributes. Explain Dodge-Romig system of determination of plan parameters for LTPD plans and AOQL plans. 15

What do you mean by “process is statistically controlled”? How to detect lack of control using a control chart? State the control limits for fraction defective control chart when population proportion is unknown and sample sizes are fixed and variable. 15

Define the reliability function and the failure rate function of a random variable denoting lifetime of a component. Establish the relation between them, if any. Prove that if is the failure rate function, then JQ h{t)dt 20

3. Explain the meanings of basic solutions and feasible solutions in a linear programming problem with m conditions and n variables. Using simplex method, solve the following linear programming problem 15

Discuss Economic Lot Size model with constant demand and variable order cycle time. 15

Consider a single-server queue system with Poisson input and exponential service time. Suppose the mean arrival rate is 3 calling units per hour, the expected service time is 0-25 hour and the maximum permissible number of calling units in the system is two. Derive the steady-state probability distribution of the number of calling units in the system and also calculate the expected number in the system
.
4. Let there be three components with independently and exponentially distributed lifetimes each with mean 1000 hours. Find the mean lifetime of the series system and the parallel system of these components.

What do you understand by an assignment problem? Mentioning the different steps of solving an assignment problem, find the solution of the following assignment problem 15

What are the different costs involved in an inventory model? Obtain the formulae for optimal order quantity and optimum variable inventory cost for the inventory model with constant demand and instantaneous supply. 15

5. Explain the difference between Paasche’s and Laspeyres’ index numbers. Check whether they satisfy the time reversal and factor reversal tests. 10

What are the objectives of analyzing seasonal movement in a time series? How does it differ from the cyclical movement? Describe the method of simple averages to deseasonalize a time series. 10

Explain different methods of collecting census data and types of error in census data. 10

Discuss registration of vital statistics in India, stating its uses and limitations. 10

Explain clearly the term ‘scaling’ as used in the problems of scholastic achievement. How does this scale differ from ordinary metre scale? 10

6.

7 Compute Age Specific Fertility Rate (ASFR) and Total Fertility Rate from the following table 15

Explain the method of population projection using logistic curve. State its limitations. 15

Obtain the general Spearman-Brown formula and explain how it is used for estimating reliability by the split-half method. What is the effect of increasing the length of a perfectly reliable test on reliability? 20

8. The following table gives the number of female births classified by age of mothers and survival rates of mothers

Age o f mothers
(in years)
Female population

No. o f female
live births
Survival rate
(per 100000)
15-19 157670 4632 58065
20-24 147624 14443 55870
25-29 124200 14058 52981
30-34 105865 8329 48963
35-39 89264 4036 44146
40-44 77887 2158 39154
45-49 61161 689 34198

Compute Gross Reproduction Rate and Net Reproduction Rate and draw your conclusion. 20

What is the difficulty in ranking individuals on the basis of total of raw scores on different tests? How to overcome this difficulty? Explain linear derived scores in this connection. 15

The following data relate to the wholesale prices of six different cereals in

January and June of a year
Cereals Weight Price in January
(in f
Price in June
(in f
1 3-68 240 290
2 2-25 174 161
3 0-42 135 165
4 0-18 128 173
5 005 133 105
6 0-19 147 180
Calculate the index number for June with January as the base by weighted
aggregative method. 15