Consider the payoff table in problem 16.Suppose that each state of nature is equally likely to occur and that two indicators, I1 and I2, are possible.The conditional probabilities for indicator I1 given the states of nature are as follows: P(I1|S1) = .1, P(I1|S2) = .2, P(I1|S3) = .3, and P(I1|S4) = .4.The expected value of sample information is:
A)0
B)5.50
C)45.50
D)90

Question

Quizplus · Accepted Answer

The expected value of perfect information (EVPI) is the difference between the expected value of the best decision under perfect information and the expected value of the best decision under uncertainty. However, since perfect information is not available in this case, we need to calculate the expected value of sample information (EVSI).

EVSI = EVPI / n, where n is the number of indicators.

EVPI = max(70, 40, 80, 60) - 50 = 30

Now we need to calculate the expected value of each indicator:

EV(I1) = 0.1(70) + 0.2(40) + 0.3(80) + 0.4(60) = 60
EV(I2) = 0.3(70) + 0.1(40) + 0.2(80) + 0.4(60) = 62

Therefore, the best indicator to choose is I2 with an EV of 62.

Finally, we can calculate the EVSI:

EVSI = (EV(I2) - 50) / 2 = (62 - 50) / 2 = 6

Therefore, the best choice is to gather information from both indicators, as the EVSI is positive and indicates a potential improvement in decision making.

Consider the Payoff Table in Problem 16