Hello, This may be a silly question but I'm not sure why the Variance of the number of claims for each Independent portfolio of policies is the same as the expected number of claims. We are not given any information about the distribution of the number of claims, except that the expected number of claims (i.e. E(N) = 10), so how do we know Var(N) = 10? It is a Poisson process so maybe has something to do with that?
The number of claims has a Poisson distribution N ~ Poi(10). We then use the formulae given on page 7 of the Tables to get the mean and variance.
