actex prac exam #5, no 10

[igelliott]

Thanks for any help.
You are given the following information about a commercial auto liability book of business:
(i) Each insured's claim count has a Poisson dist. with mean l, where l has a gamma dis. with a(alpha)=1.5 and t(theta)=0.2.
(ii) Individual claim size amounts are independent and exponentially dist. with mean 5000.
(iii) The full credibility standard is for agg. losses to be within 5% of the expected with probability 0.90.
Using classical credibility, determine the expected number of claims required for full credibility.

The book's answer gives:
For the compound dist. S with frequency N and severity Y, the full credibility standard based on number of claims required is
n0*(Var(N)*E^2(Y)+E(N)*Var(Y))/(E(N)*E^2(Y))=2381.
Isn't the whole denominator supposed to be squared, not just E(Y)?
Thanks.

[Abraham Weishaus]

If you want exposures required for full credibility, yes.

If you want expected number of claims required for full credibility (as the problem specified), no.