For a certain collection of contracts, X takes values 1, 2, 3, each with equal probabil- ities. You know that the insurer uses a recursion formula to calculate g(s) = P[S = s] and you are trying to determine what distribution is being used for N. All you have to go on is a scrap of paper on which the following appears:
g(4) = 1/3 [xg(3) + yg(2) + zg(1)],
where x, y, and z are numbers that have been smudged and are unreadable. You can, however, read enough of the numbers to definitely conclude that y is strictly less than 2x. What is the distribution of N and why? (Just identify the basic type. You do not have enough information to determine the parameters.)