Problem $2.$

You have been given a large sum of money to invest in three investment opportunities which are shown below.

The probabilities and the returns under various states of nature are shown below.

a$.$ Use the expected monetary value criterion to determine the optimal decision.

b$.$ Show that the expected opportunity loss criterion leads to the same decision recommended by the expected monetary value criterion.

c$.$ Draw the decision tree

$\backslash$table$[[$Probabilities$,0\mathrm{.}35,0\mathrm{.}45,0\mathrm{.}2],[$Decision Alternative,Market goes up$,$Market stays the same,Market goes down$],[$Stocks $($dl$),$$$100,000\mathrm{.}00,$$ $70,000\mathrm{.}00,$$$30,000\mathrm{.}00],[$Mutual Fund $($d$2),$$ $95,000\mathrm{.}00,$$$85,000\mathrm{.}00,$$$20,000\mathrm{.}00],[$Keep Cash $($d$3),$$ $73,000\mathrm{.}00,$$ $73,000\mathrm{.}00,$$$73,000\mathrm{.}00]]$