Below you are given a profit payoff table involving three decision alternatives and three states of nature. The probability of occurrence of s₁ is .1 and the probability of occurrence of s₂ is .3.
The expected value of perfect information is

Question

Below you are given a profit payoff table involving three decision alternatives and three states of nature.

The probability of occurrence of s₁ is .1 and the probability of occurrence of s₂ is .3.
The expected value of perfect information is

Quizplus · Accepted Answer

To calculate the expected value of perfect information, we need to first calculate the expected value of each decision alternative given perfect information about the state of nature. For decision alternative 1 (D1), the expected value with perfect information can be calculated by looking at the conditional outcomes for each state of nature: - If ₁ occurs (probability .1), the outcome is 17 - If ₂ occurs (probability .3), the outcome is 20 - If ₃ occurs (probability .6), the outcome is 12 The expected value of D1 with perfect information is thus: (.1)(17) + (.3)(20) + (.6)(12) = 13.6 We can repeat this process for the other decision alternatives: - Decision alternative 2 (D2) has an expected value of 12 - Decision alternative 3 (D3) has an expected value of 10.5 The expected value of perfect information is then calculated as the difference between the expected value of the best decision given perfect information and the expected value of the best decision without perfect information. The best decision given perfect information is D1, with an expected value of 13.6. The best decision without perfect information is D2, with an expected value of 9.5. Therefore, the expected value of perfect information is: 13.6 - 9.5 = 4.1 However, we are given probabilities for only two of the nine possible states of nature, so the calculations are limited. Nonetheless, we can see that D1 is likely the best choice, since its expected value with perfect information is higher than the other options, and its expected value without perfect information is also the greatest.

Below You Are Given a Profit Payoff Table Involving Three