please send me answer in type form strictly prohibited handwritten solution and answer should be correct with step by step explanation.

The aggregate loss for a portfolio is modeled as follows:

(i) Loss frequency before any coverage modifications follows a negative

binomial distribution with mean 15 and variance 90.

(ii) Loss severity before any coverage modifications follows a two-parameter

Pareto distribution with shape parameter equal to 2.3 and scale parameter

equal to 1250.

(iii) Loss frequency and severity are mutually independent.

The insurer would like to model the impact of imposing an ordinary de-

ductible of 1000 on each loss.

It is assumed that the coverage modifications will not affect the loss dis-

tribution.

(a) Determine the probability that the insurer makes at least one payment.

(b) Determine the standard deviation of the aggregate loss