Geometric distribution

Geometric distribution

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, ....

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.