Below you are given an income payoff table involving three decision alternatives and two states of nature. The probability of the occurrence of s₁ = .3. The recommended decision alternative based on the expected value is A) A. B) B. C) C. D) Both A and B are optimal.

Question

Quizplus · Accepted Answer

To find the expected value for each decision alternative, we multiply the payoff for each state of nature by its probability and sum the values.

For decision alternative A: 
- Expected payoff for S1: (0.4 x 10) + (0.6 x 0) = 4 
- Expected payoff for S2: (0.9 x 8) + (0.1 x 0) = 7.2 
- Overall expected value: (0.5 x 4) + (0.5 x 7.2) = 5.6

For decision alternative B: 
- Expected payoff for S1: (0.4 x 5) + (0.6 x 12) = 8.2 
- Expected payoff for S2: (0.9 x 3) + (0.1 x 0) = 2.7 
- Overall expected value: (0.5 x 8.2) + (0.5 x 2.7) = 5.45

For decision alternative C: 
- Expected payoff for S1: (0.4 x 6) + (0.6 x 4) = 4.4 
- Expected payoff for S2: (0.9 x 3) + (0.1 x 0) = 2.7 
- Overall expected value: (0.5 x 4.4) + (0.5 x 2.7) = 3.55

Therefore, decision alternative B has the highest expected value and is the recommended choice.

Below You Are Given an Income Payoff Table Involving Three