Use the normal approximation to find the partial credibility premium with k = 0.1 and p = 0.9 considering the claim history S1, ..., Sm of a risk of the form

, where:

a) N has a bin (n, p) distribution with n = 100 and p = 1/2, and Yj is distributed as exp () with = 1/10.

b) N has a negative binomial distribution (, p) with = 10 and p = 1/3, and Yj is distributed as exp () with = 1/10.