Suppose we toss a coin n times, and the probability of obtaining heads each time is p. Let q = 1 - p. If successive coin tosses are independent events, then the mass function describing the random variable X = number of heads is the well-known binomial random variable defined by

The z-transform for the random variable X is given by

We can now use the z-transform to determine the mean and variance of the binomial random variable. Note that

For z =1, we find

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n! P(X = j) = j!(n = 1)! P'(q)", j = 0, 1, 2,..., n