Mathematics — Probability · generating-functions-discrete
Problem
Find the generating functions, both ordinary h(z) and moment g(t), for the following discrete probability distributions.
(a) The distribution describing a fair coin.
(b) The distribution describing a fair die.
(c) The distribution describing a die that always comes up 3.
(d) The uniform distribution on the set {n,n+1,n+2,…,n+k}.
(e) The binomial distribution on {n,n+1,n+2,…,n+k}.
(f) The geometric distribution on {0,1,2,…} with p(j)=2/3j+1.