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.

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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