Uniform Uniform Company $($UUC$)$ has experienced the following workers compensation

losses $($in dollars$)$ at three of their cleaning plants over a $10-$year period shown below:

UUC is considering whether to purchase insurance or to self$-$insurance these losses.

$($a$)$ Based on the experience of plant #$1$ losses only, estimate the expected loss

and the standard deviation of the loss. $(2$ points$)$

$($b$)$ UUC is considering buying insurance from Assuring Assurance Company $($AAC$),$

an insurer that is able to pool the loss experience of plant $1$ with other firms. Assuming

that AAC is able to pool the plant $1$ losses with other firms that are independent of each

other, estimate the expected value and the standard deviation $($i$.$e$.,$ standard error$)$ of

the mean loss distribution when AAC insures $100,900,$ and $2500$ independent and homogeneous

plants. For now, disregard the loss experience of UUC's other two plants. $(4$ points$)$

$($c$)$ Calculate the premiums that AAC will charge to the three pools $($i$.$e$.,100,$

$900,$ and $2500$ exposure units$)$ if it wants to be $95\%$ confident that the premium will be

sufficient to pay for the underlying losses. $(3$ point$)$

$($d$)$ If AAC could pool an unlimited number of independent and homogeneous exposure

units, what premium would AAC charge to cover their underlying losses? Assume that AAC

wants to be $95\%$ confident that the premium charge will cover their underlying losses. $(1$

point$)$

$2)$Referring to the loss data provided above in question $1,$ calculate the variance

covariance matrix for each of the three plants owned by UUC. $(6$ points$).$

PLEASE HELP WITH #$2!!!$