試行回数 $$$n = 8$$$、成功確率 $$$p = 0.12$$$ の二項分布に従う $$$P{\left(X = 1 \right)}$$$ を求めよ
入力内容
$$$n = 8$$$、$$$p = 0.12 = \frac{3}{25}$$$、$$$x = 1$$$を用いて二項分布のさまざまな値を計算します。
解答
平均: $$$\mu = n p = \left(8\right)\cdot \left(\frac{3}{25}\right) = \frac{24}{25} = 0.96$$$A。
分散: $$$\sigma^{2} = n p \left(1 - p\right) = \left(8\right)\cdot \left(\frac{3}{25}\right)\cdot \left(1 - \frac{3}{25}\right) = \frac{528}{625} = 0.8448$$$A.
標準偏差: $$$\sigma = \sqrt{n p \left(1 - p\right)} = \sqrt{\left(8\right)\cdot \left(\frac{3}{25}\right)\cdot \left(1 - \frac{3}{25}\right)} = \frac{4 \sqrt{33}}{25}\approx 0.919130023446085.$$$A
$$$P{\left(X = 1 \right)}\approx 0.392328572515123$$$A
$$$P{\left(X \lt 1 \right)}\approx 0.35963452480553$$$A
$$$P{\left(X \leq 1 \right)}\approx 0.751963097320653$$$A
$$$P{\left(X \gt 1 \right)}\approx 0.248036902679347$$$A
$$$P{\left(X \geq 1 \right)}\approx 0.64036547519447$$$A