This practice problem gives us E(X) = 11 and E(X^2) = 121 and asks for us to find probability fn and cdf.

Initially I was thinking we could use some identities of the probability generating function like P"(1) = E(X^2) - E(X) and P'(1) = E(X), but I'm running into a mental wall where I'm positive that you can't work it out unless you know how X is distributed (as in is it a poisson, binomial, etc).

Any advice?