# 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.

If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please write it in the comments below.

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

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