Question

For a particular policyholder, the number of losses during the next year, N, follows a

Poisson distribution with ?=2.5.

If a loss occurs, the amount of each loss, X, has the following distribution listed below.

The number of losses is independent of the amount of a loss.

x	p(x)
120	0.40
160	0.45
300	0.15

Let S represent aggregate losses during the next year.

(a) Calculate E(S).

(b) Determine Var(S).

(c) Calculate P(S < 250).

Answer 1

Here

So,

Also,

and,

So,

a)

If , then,

b)

If , then,

c)

Required probability =