Question

The following payoff table shows the cost for a decision analysis problem with two decision alternatives and three states of nature

decision alternative. s1 s2 s3
d1 230 160 140
d2 210 180 155
If the decision maker estimates the following probabilities for the three states of nature; P(s1) = 0.3, P(s2) = 0.2 and P(s3) = 0.5
Calculate the expected value with perfect information (EVwPI).

Answer 1

To calculate the expected value with perfect information (EVwPI), you need to multiply each payoff by its corresponding probability and sum up the results. In this case, the expected value with perfect information is higher for decision alternative d2.

Step-by-step explanation:

To calculate the expected value with perfect information (EVwPI), you need to multiply each payoff by its corresponding probability and sum up the results. In this case, we have two decision alternatives (d1 and d2) and three states of nature (s1, s2, and s3). Using the given probabilities (P(s1) = 0.3, P(s2) = 0.2, and P(s3) = 0.5), we can calculate the expected values for each decision alternative and then compare them.

The expected value for d1 can be calculated as: (230 * 0.3) + (160 * 0.2) + (140 * 0.5) = 69 + 32 + 70 = 171.

The expected value for d2 can be calculated as: (210 * 0.3) + (180 * 0.2) + (155 * 0.5) = 63 + 36 + 77.5 = 176.5.

Therefore, the expected value with perfect information (EVwPI) is higher for decision alternative d2, which suggests that d2 would be the likely outcome in this case.