derivation of the mean and variance of the geometric distribution is given

in the following links

mean of the geometric distribution ---------mean of the geometric distribution

variance of the geometric distribution ---------------variance of the geometric distribution

The pdf used is f(x) = p q^(x-1) , x = 1,2,3,4,... where q=1-p

in finding E(X) we use the binomial series of (1-u) ^(-2)

for E(X^2) we manipulate it into E[X(X-1)] and then use the

binomial series for (1-u)^(-3)

mean = 1/p

variance = q/[p^2]

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