Kalkulator rozkładu beta

Oblicz różne wartości dla rozkładu beta z $\alpha = 2$, $\beta = 3$ i $x = 0.5$.

Średnia: $\mu = \frac{\alpha}{\alpha + \beta} = \frac{2}{5} = 0.4$A.

Wariancja: $\sigma^{2} = \frac{\alpha \beta}{\left(\alpha + \beta\right)^{2} \left(\alpha + \beta + 1\right)} = \frac{1}{25} = 0.04$A.

Odchylenie standardowe: $\sigma = \sqrt{\frac{\alpha \beta}{\left(\alpha + \beta\right)^{2} \left(\alpha + \beta + 1\right)}} = \frac{1}{5} = 0.2$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