# Geometric Distribution Calculator

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

## 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**