# Beta Distribution Calculator

## Calculate probabilities of the beta distribution step by step

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**