e-DTN-L-TUB


ITime Allowed: Maximum Marks: 300 I
,..
.INSTRUCTIONS
Each question is ,both, in Hindi and in English. Answers be wnttenirz, the medium specified in the'AdrriissionCerlificate issued to you, which must stated clearly on the cover the space proVided for. the purpose. No marks will he
,given·for the answers. writt?n in a mec:lium other than that specified in the Admission Certificqfe.
Candid(2tes should attempt Question Nos. 1 and 5 which are compulsory, and any three of the remaining questipns. selecting· at least one question from each 'Section. The number of marks c.arried by each question is incilicdted the end of the question. Assume suitable Clata if considered necessary and· indicate the same· clearly. ,Symbols/Notations used carry usual :[1leanings, unless indicated., Char,ts/Figures, tc? be drawn in the answer-book itself and not .on separate graph sheet.
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Section-A

1. Answer the following 12x5=60

(a)For a finite irreducible 'aperiodic Markov chain with n-step transition probabilities show that lim n exists,and is independenI of the initial" state.

Describe briefly about the queue system G Obtain the expect number of persons In the system from

State the procedure for double sampling attributes plan for lot disposition. Also derive its OC and ASN functions.

Use simplex method to solve the following LPP

Maximize Z Xl -x2 +3x3
subject to
Xl +x2 +x3
2xl -X3
2xl -2x2
sO X3 0
Discuss an inventory model with probabilistic demand.
2. Justify the use of ,artificial variables in obtainitI,g'LPP. When should slack and' surplus variables be. used for solving linear programming problem? 10
Explain the economic cost project models used in. queueing-theory. 20
state the limitations for theory. Following is the pay-off matrix 'for .players A and B. 'dominance' property, obtain the optimum strategies for. botl). the and determine of <the. 10
<img src='./qimages/1057-2c.jpg'>

Explain the, concept, of recurrence and transience in the case of finite Markov chains ·20
3 Determine the optimal strategies for the game with the following pay-off matrix.: 25
<img src='./qimages/1057-3a.jpg'>
A 'supermarKet has ·2 girls ringing up sales at the counters., If the srrvice time for each customer ex,:ponential with mean 4 minutes and.if people:arrive in a Poisson fashion at the rate of 10 per hour­
what is "the probability of having to
wait for service;
what is the expected percentage of
idle time for each girl? 20
A·.company uses annually 24000 units of a raw material which. costs 1·25 per unit: Placing each order costs 22·5 and_ .title carrying cost is 5·40/0 per of oh average (inventory. Find the economic' lot size and the total inventory cost"(including cost of material). 15
4. The-following table shows all the
,;necessary information on. the. available
'supply to each warehouse, the
i requirements for each the
unit transportation 'cost from each
warehouse to each market:
<img src='./qimages/1057-4a.jpg'>

The shipping clerk :has worked out following schedule from experience
12 units from A to 11
1unit from A to III
9 units from a to lv
15 units from B to III
1 unit from C to 1I1
7 units fromC to 1
Check and verifying if the clerk has the optimal schedule.
Find. the optimal schedule and the minimum total shipping 25
Construct a control chart X and R from the following data on 'the basis of 'samples of 5 being taken 'every hour (each set 5 1;>een 'arranged in ascending ,order of magnitude). Comment on the 'stateof control. What
will be the. future coIitrol limits for
and: R charts? 20

42 -42 19 36 .42 ·51 60 18 15 69 64 61
65 45 24 54 51· . 74. ,20 30 ,109 90 .78
75 68 80 69 57 75 .72 27 39 .117: 93 94
78 72 -81 77 59 78 95 42, 54 118 109 109
87 90 81 84 78 132 1'35 60 62 153 112 139
Table, Value For' n·=5 A2 O· 57·7, D3 D4 =2·11
Explain the different "types of redundancies and, In improving'Athe :reliability ,of ·'a .system.

Section-B

5. Answer the following: 12x5=60
Explain the identification problem, and state the rank and order conditions for identifying model equation. Show that these conditions are ;necessary and sufficient.,

Define and describe ,quasi-stable theory of population.

State Laspeyres and ,Paasche's index number of prices, and examine whether they satisfy the various tests for index numbers.

Explain the concept for moving average model arid autoregressive moving average model

Explain how the infant mortality rate is constructed;
6. Explain Durbin -Watson test for. auto correlation under a general linear ,model. 20
Explain in"'detail two-stage least squares method for estimation 20
Describe in detail the .problem of multicollinearity with all. example.• . . 20

7. Explain in detail the three tests for flXed base index numbers. 25
Project Weibull distribution as a failure model. Derive its hazard function. What,. is a bathtub curve? 20
'Explain different measures of mortality. Briefly discuss about the procedures for finding standardization of rates through direct and indirect -methods. 15
8. Specify the time and factor reversal tests for a price index number. Illustrate by a standard price index number which satisfies both the tests. Prove your claim. 25
Write a note on Central Statistical Organization. 20
Write briefly on 15 Methods for collection of official statistics in India Reliability and limitations of data collection