Is it correct? From the tables, the PGF of the Negative Binomial has an "s" in the numerator as well as the denominator. This doesn't appear to be reflected in the solution. This would mean that when combining the PGFs, there is a (1-q+qt)^M on the top line aswell as the bottom. Please clarify. Thanks Jooser
The answer is using the Type 2 negative binomial distribution, which doesn't have the s on the numerator. Unless we have a good reason to believe there will be at least k claims, the type 2 makes more sense in the context of claim numbers, so we can have n = 0, 1, 2, ... instead of n = k, k+1, k+2, ... This question had me puzzled too, I think it is explained somewhere later on in the course.
