Allen Young has always been proud of his personal investment strategies and has done very well over the last several years. He invests primarily in the stock market. Over the last several months, however, Allen has become very concerned about the stock market as a good investment. In some cases, it would have been better for Allen to have his money in a bank than in stock market. During the next six months, Allen must decide whether to invest $$1,000$ in the stock market or in a six$-$month certificate of deposit $($CD$)$ at an interest rate of $10\%.$ If the market is good, Allen believes that he could get a $14\%$ return on his money. With a fair market, he expects to get an $8\%$ return. If the market is bad, he will most likely get no return at all in other words; the return would be $0\%.$ Allen estimates that the probability of a good market is $0\mathrm{.}4,$ the probability of a fair market is $0\mathrm{.}4,$ and the probability of a bad market is $0\mathrm{.}2,$ and he wishes to maximize his long$-$run average return.

$($a$).$ Develop a decision table for this problem.

$($b$).$ What is the best decision using EMV?

$($c$).$ Determine EOL and the best strategy.

$($d$).$ What is the expected value of perfect information?

$($e$).$ What type of decision is Allen facing?

$($f$).$ What is sensitivity analysis and how is it beneficial to a decision maker?

Please answer the questions fully labeling all parts