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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:
- P(X = n) = (1 - p)n - 1p
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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