試行回数 $$$n = 2$$$、成功確率 $$$p = 0.09$$$ の二項分布に従う $$$P{\left(X = 1 \right)}$$$ を求めよ

$$$n = 2$$$、$$$p = 0.09 = \frac{9}{100}$$$、$$$x = 1$$$を用いて二項分布のさまざまな値を計算します。

平均: $$$\mu = n p = \left(2\right)\cdot \left(\frac{9}{100}\right) = \frac{9}{50} = 0.18$$$A。

分散: $$$\sigma^{2} = n p \left(1 - p\right) = \left(2\right)\cdot \left(\frac{9}{100}\right)\cdot \left(1 - \frac{9}{100}\right) = \frac{819}{5000} = 0.1638.$$$A

標準偏差: $$$\sigma = \sqrt{n p \left(1 - p\right)} = \sqrt{\left(2\right)\cdot \left(\frac{9}{100}\right)\cdot \left(1 - \frac{9}{100}\right)} = \frac{3 \sqrt{182}}{100}\approx 0.404722126896961.$$$A

$$$P{\left(X = 1 \right)} = 0.1638$$$A

$$$P{\left(X \lt 1 \right)} = 0.8281$$$A

$$$P{\left(X \leq 1 \right)} = 0.9919$$$A

$$$P{\left(X \gt 1 \right)} = 0.0081$$$A

$$$P{\left(X \geq 1 \right)} = 0.1719$$$A