Solve these as if it were in excel. Show functions used please.

Question $1$

The number of claims received by an insurance company in a year is Negative Binomial with $r=23$ and $p=0\mathrm{.}51.$ The claim amounts $($severity$)$ are independent of one another and are distributed lognormally with parameters $=7\mathrm{.}97$ and $=1\mathrm{.}26.$ Define $S$ to be the random variable for the totalamount of claims paid in a year. Find the pure premium $($actuarially fair premium$)$ and variance of total claims in a year.

Question $2$

Suppose you are the risk manager for Allied Lines, a moving company headquartered Rapids, and you self$-$insure the property $-$ damage liability risk you face from the of $376$ moving trucks. Assume each truck's loss distribution is independent and identically

distributed and, based upon historical data, you know the mean of the loss distribution for one truck is $$2000$ and the variance of loss is $26,325,000.$ You want to establish a reserve to cover the losses. How much money should you put in the reserve if you want to be $90$ percent certain that there will he enough funds availahle to nav all loss obligations?