The Geometric distribution reference article from the English Wikipedia on 24-Jul-2004 (provided by Fixed Reference: snapshots of Wikipedia from wikipedia.org)

Geometric distribution

In mathematics, the geometric distribution is a discrete probability distribution -- the probability distribution of the number of Bernoulli trials needed to get one success, if the probability of success is p. The probability that the first success is on the nth trial is:

for n = 1, 2, 3, .... This sequence of probabilities is a geometric sequence.

The expected value of a geometrically distributed random variable is 1/p and the variance is (1 − p)/p².

It is the special case of the negative binomial distribution in which r = 1. Like its continuous analogue (the exponential distribution), the geometric distribution is memoryless; in fact, it is the only memoryless discrete distribution.

See also negative binomial distribution.

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