Mathematics — Probability · generating-functions-discrete
Problem
Let p be a probability distribution on {0,1,2} with moments μ1=1, μ2=3/2.
(a) Find its ordinary generating function h(z).
(b) Using (a), find its moment generating function.
(c) Using (b), find its first six moments.
(d) Using (a), find p0, p1, and p2.