Page 129 - DMTH404_STATISTICS

Unit 8: Expected Value with Perfect Information (EVPI)

Further, equation (3) gives Notes

l l
P (D ³ A + ) 1 < or 1 P- (D < A + ) 1 <
p + l p + l

l p
1
or P (D < A + ) 1 > - or P (D £ A ) > .... (5)
p + l p + l
Combining (4) and (5), we get
p
P (D £ A - ) 1 £ < P (D £ A ) .
p + l
Writing the probability distribution, given in example 20, in the form of less than type cumulative
probabilities which is also known as the distribution function F(D), we get

D
Units demanded ( ) : 5 6 7 8 9
F ( ) : 0.1 0.3 0.6 0.85 1.00
D
p 3
We are given p = 3 and l = 2 ,  = = 0.6
p + l 5
Since the next cumulative probability, i.e., 0.85, corresponds to 8 units, hence, the optimal order
is 8 units.

8.2 Use of Subjective Probabilities in Decision Making

When the objective probabilities of the occurrence of various states of nature are not known, the
same can be assigned on the basis of the expectations or the degree of belief of the decision
maker. Such probabilities are known as subjective or personal probabilities. It may be pointed
out that different individuals may assign different probability values to given states of nature.
This indicates that a decision problem under uncertainty can always be converted into a decision
problem under risk by the use of subjective probabilities. Such an approach is also termed as
Subjectivists's Approach.

Example 21:
The conditional payoff (in Rs) for each action-event combination are as under:

Action ®
1 2 3 4
Event ¯
A 4 - 2 7 8
B 0 6 3 5
C - 5 9 2 - 3
D 3 1 4 5
E 6 6 3 2

(i) Which is the best action in accordance with the Maximin Criterion?
(ii) Which is the best action in accordance with the EMV Criterion, assuming that all the
events are equally likely?

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