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.

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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