Question $1(9$ marks$)$

True or False? Explain your answer with calculations $($if necessary$).$

a$.$ Most individuals primarily engage with the financial system through direct investments in stock markets rather than using institutions like banks or mutual funds.

b$.$ Adverse selection occurs when borrowers take on riskier projects after securing a loan, knowing lenders cannot monitor their actions.

c$.$ In a U$.$S$.$ Treasury auction, if non$-$competitive bids total $$2$ billion and competitive bids are as follows: $$3$ billion at $1\mathrm{.}5\%,$$$4$ billion at $1\mathrm{.}6\%,$ and $$3$ billion at $1\mathrm{.}7\%,$ and the Treasury is offering $$10$ billion in securities$,$ the stop$-$out rate will be $1\mathrm{.}5\%.$

Question $2(14$ marks$)$

Company Y would like to hire Lisa to manage Sunshine operations. The profits from the operations depend partially on how hard Lisa works, as follows:

$\backslash$table$[[,$Probabilities$],[,\backslash$table$[[$Profit $=$