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

Question: 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.

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

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