貝他分配計算器

使用 $$$\alpha = 2$$$、$$$\beta = 3$$$ 與 $$$x = 0.5$$$ 計算貝他分佈的各種數值。

平均值：$$$\mu = \frac{\alpha}{\alpha + \beta} = \frac{2}{5} = 0.4$$$A。

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

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