Consider an investment $x$ whose payoff is uniformly distributed over $-15,45$ and an$-$

other $Y$ whose payoff is uniformly distributed over $-15,25.$ Evaluate the investments

using

$($a$)$ the Expected Value criterion,

$($b$)$ the Mean Variance criterion $($with $k=0\mathrm{.}5),$

$($c$)$ the Safety$-$First Criterion with threshold $t=-1$ and $k=0\mathrm{.}5.$

$($d$)$ In each of $($a$),($b$)$ and $($c$)$ above, state with justification which investment you

would choose.