For any risk in a population the number of losses N in a year has a Poisson distribution with parameter G. Individual loss amounts X for a selected risk are independent of N and are iid with exponential distribution F(x) = 1e^(x/). There are three types of risks.. A risk was selected at random from the population below and all losses were recorded over a five-year period. The total amount of losses over the five-year period was 6,000.

Use Buhlmann credibility to estimate the annual expected aggregate loss for the risk.

Risk type % of population Poisson parameter Exponential parameter A 25% G=1.5 =1000

B 45% G=1.25 =1500

C 30% G=2.5 =2000