# Geometric Distribution Calculator

The calculator will find the simple and cumulative probabilities, as well as the mean, variance, and standard deviation of the geometric distribution.

Related calculator: Exponential Distribution Calculator

There are two types of geometric distributions: either $X$ is the number of trials up to and including the first success, or $X$ is the number of trials (failures) until the first success.

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Calculate the various values for the geometric distribution with $n = 7$ and $p = 0.5 = \frac{1}{2}$ (include a success trial).

Mean: $\mu = \frac{1}{p} = \frac{1}{\frac{1}{2}} = 2$A.

Variance: $\sigma^{2} = \frac{1 - p}{p^{2}} = \frac{1 - \frac{1}{2}}{\left(\frac{1}{2}\right)^{2}} = 2$A.

Standard deviation: $\sigma = \sqrt{\frac{1 - p}{p^{2}}} = \sqrt{\frac{1 - \frac{1}{2}}{\left(\frac{1}{2}\right)^{2}}} = \sqrt{2}\approx 1.414213562373095$A.

$P{\left(X = 7 \right)} = 0.0078125$A

$P{\left(X \lt 7 \right)} = 0.984375$A

$P{\left(X \leq 7 \right)} = 0.9921875$A

$P{\left(X \gt 7 \right)} = 0.0078125$A

$P{\left(X \geq 7 \right)} = 0.015625$A