Geometric Distribution Calculator

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

Number of trials $$$n$$$:

Probability of success $$$p$$$:

Include a success trial?

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