Let X be a discrete random variable with the nonnegative integers as values.
is a probability generating function of X, inasmuch as the coefficient of tj gives P[X = n. Find g[tX] for the random variable of Probs. 6 and 7.
Probs. 6
A fair coin is tossed until a head appears. Let X denote the number of tosses required.
(a) Find the density function of X.
(b) Find the mean and variance of X.
(c) Find the moment generating function (m.g.f.) of X.
Probs. 7
A has two pennies; B has one. They match pennies until one of them has all three. Let X denote the number of trials required to end the game.
(a) What is the density function of X?
(b) Find the mean and variance of X.
(c) What is the probability that B wins the game?