# Beta Distribution Calculator

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

## Your Input

**Calculate the various values for the beta distribution with $$$\alpha = 2$$$, $$$\beta = 3$$$, and $$$x = 0.5$$$.**

## Answer

**Mean: $$$\mu = \frac{\alpha}{\alpha + \beta} = \frac{2}{5} = 0.4$$$A.**

**Variance: $$$\sigma^{2} = \frac{\alpha \beta}{\left(\alpha + \beta\right)^{2} \left(\alpha + \beta + 1\right)} = \frac{1}{25} = 0.04$$$A.**

**Standard deviation: $$$\sigma = \sqrt{\frac{\alpha \beta}{\left(\alpha + \beta\right)^{2} \left(\alpha + \beta + 1\right)}} = \frac{1}{5} = 0.2$$$A.**

**$$$P{\left(X = 0.5 \right)} = 0$$$A**

**$$$P{\left(X \lt 0.5 \right)} = 0.6875$$$A**

**$$$P{\left(X \leq 0.5 \right)} = 0.6875$$$A**

**$$$P{\left(X \gt 0.5 \right)} = 0.3125$$$A**

**$$$P{\left(X \geq 0.5 \right)} = 0.3125$$$A**