For a collective risk model the number of losses, N, has a Poisson distribution with = 25 and the common distribution of the individual losses has the following properties:

(a) E[X] = 95

(b) E[X 50] = 40

(c) P(X 50) = 0.20

(d) E[X^2 |X 50] = 4000.

(e) E[X^2 ] = 10400.

There is an ordinary deductible of 50 per loss. Calculate the variance of the aggregate losses of the insurance.