An investment yields a random return $R$ with probability mass function.

$P(R=x\%)=0\mathrm{.}1x,$ where $x=2,3,5.$

Calculate the risk in this investment using :

$($a$)(3$ points$)$ the downside semi$-$variance of return.

$($b$)(3$ points$)$ the shortfall probability based on a benchmark return of $4\%.$

$($c$)(4$ points$)$ the expected shortfall below a benchmark return of $4\%$