A cost payoff table is given as

Cost Payoff Table

a. The optimistic strategy is:

b. The pessimistic strategy is:

c. The minimax regret strategy is:

d. If the P(s₁)=0 .2, P(s₂)=0 .5, and P(s₃)=0.3, respectively, then the expected payoff strategy is:

e. The expected value of perfect information is:

f. If the conditional probabilities obtained from sample information I are P(I s₁)= 0.1, P(I s₂)= 0.05, P(I s₃)= 0.2, compute the revised or posterior probabilities P(s₁ I), P(s₂ I) and P(s₃ I).

P(Sj I)

Sj	P(Sj)	P(ISj)	P(Sj) P(ISj)	P(SjI)
S1	0.20	0.10	........	...........
S2	0.50	0.05	...........	...........
S3	0.30	0.20	............	............
	1.00		...........	............

g. Compute expected payoffs for each decision using the revised probabilities, obtained from part f. What choice should be made? .........

State of Nature \begin{tabular}{|c|c|c|c|} \hline Decision & s1 & s2 & s3 \\ \hline d1 & 421 & 852 & 567 \\ \hline d2 & 1172 & 336 & 1125 \\ \hline d3 & 275 & 737 & 1035 \\ \hline \end{tabular}