Hi all, Would you be able to help explain how to calculate the probability that, in any given year, there are no claims that exceed the retention level? I couldn't quite work out why the solution was exp(-lambda)*exp(lambda*(prob that an individual claim do not exceed the retention lvl)) Thanks in advance for your help!
Hi Laura We know from part (v) that the probability that a claim is less than the retention is 0.9332. So if there were x claims then the probability that they were all less than the retention is 0.9332^x. We then need to work out the probability that x is the number of claims. As this is Poisson then from page 7 of the Tables we have exp(-lambda) lambda^x /x!. We then multiply these together and sum over all the values of x. Best wishes Mark
