How are the mean and standard deviation calculated for a geometric random variable?

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Feb 3, 2016

A geometric random variable is one which measures the number of trials that must be performed before we get a "success".

If the probability of success for each trial is p, then the probability that the last of k trials is the first success is

$P r \left(X = k\right) = {\left(1 - p\right)}^{k - 1} p$

i.e. (k-1) failures, with probability 1-p, and one success, with probability p.

The mean is given by $\frac{1}{p}$, the standard deviation by $\frac{\sqrt{1 - p}}{p}$.

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