$6.$ An insurance portfolio produces N claims with the following distribution: n Pr$($N $=$ n$)0120\mathrm{.}10\mathrm{.}50\mathrm{.}4$ Individual claim amounts have the following distribution: $00\mathrm{.}7100\mathrm{.}2200\mathrm{.}1$ Individual claim amounts and counts are independent. Stop$-$loss insurance is purchased with an aggregate deductible of $400\%$ of expected aggregate claims. Calculate the net stop$-$loss premium.$($b$)$ Losses on an insurance portfolio have the following distribution:

The losses in each range are uniformly distributed.

$($i$)$ State the actual value of loss at the ${95}^{th}$ percentile. Then, explain what this value

represents.

$($ii$)$ Using your answer in part $($b$)($i$),$ define the $95\%$ Tail Value$-$at$-$Risk. Then,

calculate its value.