Page 134 - DMTH404_STATISTICS

Statistics

Notes 40. The payoffs of three acts A, B and C and the states of nature P, Q and R are given as :

Payoffs ( Rs )
in
of
States Nature A B C
P - 35 120 - 100
Q 250 - 350 200
R 550 650 700

The probabilities of the states of nature are 0.5, 0.1 and 0.4 respectively. Tabulate the
Expected Monetary Values for the above data and state which can be chosen as the best act?
Calculate expected value of perfect information also.
41. A manufacturing company is faced with the problem of choosing from four products to
manufacture. The potential demand for each product may turn out to be good, satisfactory
or poor. The probabilities estimated of each type of demand are given below:

of
of
Probabilities type demand
Product Good Satisfactory Poor
A 0.60 0.20 0.20
B 0.75 0.15 0.10
C 0.60 0.25 0.15
D 0.50 0.20 0.30

The estimated profit (in Rs) under different states of demand in respect of each product
may be taken as:

A 40,000 10,000 1,100
B 40,000 20,000 - 7,000
C 50,000 15,000 - 8,000
D 40,000 18,000 15,000

Prepare the expected value table and advise the company about the choice of product to
manufacture.

Answers: Self Assessment

1. Marginal analysis 2. probability values
3. decision tree diagrams 4. chance node

8.8 Further Readings

Books Introductory Probability and Statistical Applications by P.L. Meyer

Introduction to Mathematical Statistics by Hogg and Craig
Fundamentals of Mathematical Statistics by S.C. Gupta and V.K. Kapoor

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