Geometric Distribution Calculator
Calculate P(X=k) = (1-p)^(k-1) * p.
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Enter the probability of success on each trial and the trial number you are interested in. The calculator computes the probability that the first success occurs on exactly that trial, plus cumulative probability and distribution statistics.
About This Calculator
The geometric distribution models the number of trials needed to get the first success. If each trial has success probability p, then P(X=k) = (1-p)^(k-1) * p. It is the discrete analog of the exponential distribution and shares the memoryless property among discrete distributions.
Frequently Asked Questions
What is the mean of the geometric distribution?
The mean is 1/p. If the probability of success is 0.2, you expect to need 5 trials on average to get the first success.
Is the geometric distribution memoryless?
Yes. It is the only discrete distribution with the memoryless property. Past failures do not affect the probability of success on the next trial.
What is the difference between geometric and negative binomial?
The geometric distribution is a special case of the negative binomial with r=1 (first success). The negative binomial models the trial number of the rth success.