Let X $$ U$(0,$ b$).$

$($a$)$ Determine the pure premium and the expected$-$value premium

with loading $.$

$($b$)$ Determine the variance premium and standard$-$deviation premium

with loading $.$

$($c$)$ Determine VaR $($X $),$ and calculate CTE $($X $)$ using equation

$(4\mathrm{.}19).$

$($d$)$ Calculate CTE $($X $)$ using equation $(4\mathrm{.}17)$ and verify that the

answer is the same as in $($c$).$

$($e$)$ Calculate CVaR $($X $)$ using equation $(4\mathrm{.}13)$ and TVaR $($X $)$ using

equation $(4\mathrm{.}23)$