Question

**Question 1**

**Suppose that each individual in a large insurance portfolio**

** incurs losses according to an exponential distribution with mean (1/**** λ), where λ varies over ****the portfolio according to a G(****α, δ) ****mixing distribution. The respective densities of the two distributions are given by:**

**(a) Show that the marginal distribution of losses follows a Pareto distribution, i.e. P(****α, δ)**

**(b) ****Use the mixing formulation of the Pareto to deduce that if X~P(****α, δ), then E(X) = α / (δ – 1)**

Statistics and Probability

Question 1Suppose that each individual in a large insurance portfolio