Let p be a probability distribution on {0, 1, 2} with moments 1 = 1, 2 = 3/2. (a) Find its ordinary generating function h(z).

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.