Let N be the number of claims an insurance company receives

Let N be the number of claims an insurance company receives per week.

-N is modeled by a Poisson random variable with mean , which itself is a random variable.

- has a Gamma distribution ~(,).

-Claims are modeled as Gamma random variables: I’th claim Y_i~(1000,2)

-The aggregate losses is S = ⁿ_i=1 Y_i

Find E(N), Var(N), E(Y_i), Var(Y_i).

Find E(S) and Var(S).

Solution

E(N) = V(N) =

=1000,=2

E(Yi)= / = 500 V(Yi) = /^2 = 250

S = ni=1  Yi Not clear about the this text.