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