The Following Payoff Table Shows the Profit for a Decision

Essay

The following payoff table shows the profit for a decision problem with three states of nature and three decision alternatives: $$\begin{array} { | l | c | c | c | } \hline \text { Decision } & { \text { State of Nature } } \\\hline \text { Alternative } & \boldsymbol { s 1 } & \boldsymbol { s 2 } & \boldsymbol { s 3 } \\\hline \boldsymbol { A 1 } & 7 & 3 & 4 \\\hline \boldsymbol { d } & 2 & 4 & 5 \\\hline \boldsymbol { d } & 8 & 2 & 3 \\\hline\end{array}$$
a. Suppose P(s₁) = 0.1, P(S₂) = 0.3, and P(S₃) = 0.6. What is the best decision using the expected value approach?
b. Suppose that the probability of sate of nature, s₁, s₂, and s₃ changes to 0.4, 0.2, and 0.4, respectively. What is the best decision using the expected value approach in this case?