$1.$ In addition, you know that the correlation between the two stocks is $0\mathrm{.}10$ ; the standard deviations for stock A and B are $\backslash (20\backslash \%\backslash )$ and $\backslash (25\backslash \%\backslash ),$ respectively. An investor X $\text{'}$s risk preferences are characterized by the following utility function: $\backslash (\backslash$mathrm$\{$U$\}=\backslash$mathrm$\{$E$\}(\backslash$mathrm$\{$r$\})-0\mathrm{.}5\backslash$mathrm$\{$~A$\}\backslash$sigma$^\{2\}\backslash ).$ Assume that for an investor X with risk aversion level $\backslash (\backslash$mathrm$\{$A$\}=4\backslash ).$ There are also risk$-$free assets available in the market. The investor X is considering building a portfolio consisting of the two stocks and the risk$-$free assets. The investor is willing to spend $\backslash (\backslash$$ $10,000\backslash )$ on this portfolio. How would the investor X allocate the $\backslash (\backslash$$ $10,000\backslash )$ in the stocks and risk$-$free assets to best serve the investor's interest?

$2.$ Now there is another investor $\backslash ($ Y $\backslash )$ with the same utility function and risk aversion level as the investor X$.$ S$/$he is considering investing $\backslash (\backslash$$ $10,000\backslash )$ in a portfolio consisting of the market portfolio and the risk$-$free assets. The market portfolio has a standard deviation of $\backslash (15\backslash \%\backslash ).$ How would you allocate the $\backslash (\backslash$$ $10,000\backslash )$ in the market portfolio and the risk$-$free assets to best serve Y$\text{'}$s welfare? Compared to your answer in part ii$),$ which investor's strategy is better, X or Y$?$ Why?