0
$\begingroup$

Assume the total number of claims $N$ in a given year faced by an insurance company is a random variable following a Poisson distribution with mean $\lambda$. Assume the amount of claims$ Y_1, Y_2,...$, are independent random variables having the same mean $\mu$ and variance $\sigma^2$ . Also assume that the total number of claims and the claim sizes are independent. Let $S = \Sigma_{i=1}^N Y_i $ be the total amount of the claims faced by the insurance company during the given year. Find the mean and variance of $S$.

$\endgroup$
  • $\begingroup$ Could you add what you have tried so far? $\endgroup$ – Jerry Apr 9 '13 at 18:29
  • $\begingroup$ @Jerry I have no idea since $S$ involves many variables. $\endgroup$ – N Zhang Apr 9 '13 at 18:38
  • $\begingroup$ Really? In my experience $N$ isn't THAT big. Most numbers are bigger than it! ;) $\endgroup$ – Tyler Apr 9 '13 at 18:40
0
$\begingroup$

$S$ has a compound poisson distribution. See the link below. http://en.wikipedia.org/wiki/Compound_Poisson_distribution

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.