試行回数 $$$n = 10$$$、成功確率 $$$p = 0.1$$$ の二項分布に従う $$$P{\left(X = 1 \right)}$$$ を求めよ

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

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

分散: $$$\sigma^{2} = n p \left(1 - p\right) = \left(10\right)\cdot \left(\frac{1}{10}\right)\cdot \left(1 - \frac{1}{10}\right) = \frac{9}{10} = 0.9$$$A.

標準偏差: $$$\sigma = \sqrt{n p \left(1 - p\right)} = \sqrt{\left(10\right)\cdot \left(\frac{1}{10}\right)\cdot \left(1 - \frac{1}{10}\right)} = \frac{3 \sqrt{10}}{10}\approx 0.948683298050514.$$$A

$$$P{\left(X = 1 \right)} = 0.387420489$$$A

$$$P{\left(X \lt 1 \right)} = 0.3486784401$$$A

$$$P{\left(X \leq 1 \right)} = 0.7360989291$$$A

$$$P{\left(X \gt 1 \right)} = 0.2639010709$$$A

$$$P{\left(X \geq 1 \right)} = 0.6513215599$$$A