Geometric Distribution Calculator

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

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: $$$\sigma = \sqrt{\frac{1 - p}{p^{2}}} = \sqrt{\frac{1 - \frac{1}{2}}{\left(\frac{1}{2}\right)^{2}}} = \sqrt{2}\approx 1.4142135623731$$$A.

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

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

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

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

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