試行回数 $$$n = 7$$$、成功確率 $$$p = 0.1$$$ の二項分布に従う $$$P{\left(X = 1 \right)}$$$ を求めよ

$$$n = 7$$$、$$$p = 0.1 = \frac{1}{10}$$$、$$$x = 1$$$を用いて二項分布のさまざまな値を計算します。

平均: $$$\mu = n p = \left(7\right)\cdot \left(\frac{1}{10}\right) = \frac{7}{10} = 0.7$$$A。

分散: $$$\sigma^{2} = n p \left(1 - p\right) = \left(7\right)\cdot \left(\frac{1}{10}\right)\cdot \left(1 - \frac{1}{10}\right) = \frac{63}{100} = 0.63$$$A.

標準偏差: $$$\sigma = \sqrt{n p \left(1 - p\right)} = \sqrt{\left(7\right)\cdot \left(\frac{1}{10}\right)\cdot \left(1 - \frac{1}{10}\right)} = \frac{3 \sqrt{7}}{10}\approx 0.793725393319377.$$$A

$$$P{\left(X = 1 \right)} = 0.3720087$$$A

$$$P{\left(X \lt 1 \right)} = 0.4782969$$$A

$$$P{\left(X \leq 1 \right)} = 0.8503056$$$A

$$$P{\left(X \gt 1 \right)} = 0.1496944$$$A

$$$P{\left(X \geq 1 \right)} = 0.5217031$$$A