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Geometric Distribution Calculator

Calculate probabilities of the geometric distribution step by step

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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Your Input

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

Answer

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