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試行回数 $$$n = 12$$$、成功確率 $$$p = 0.1$$$ の二項分布に従う $$$P{\left(X = 8 \right)}$$$ を求めよ
入力内容
$$$n = 12$$$、$$$p = 0.1 = \frac{1}{10}$$$、$$$x = 8$$$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: $$$\mu = n p = \left(12\right)\cdot \left(\frac{1}{10}\right) = \frac{6}{5} = 1.2$$$A。
分散: $$$\sigma^{2} = n p \left(1 - p\right) = \left(12\right)\cdot \left(\frac{1}{10}\right)\cdot \left(1 - \frac{1}{10}\right) = \frac{27}{25} = 1.08$$$A.
標準偏差: $$$\sigma = \sqrt{n p \left(1 - p\right)} = \sqrt{\left(12\right)\cdot \left(\frac{1}{10}\right)\cdot \left(1 - \frac{1}{10}\right)} = \frac{3 \sqrt{3}}{5}\approx 1.039230484541326.$$$A
$$$P{\left(X = 8 \right)} = 0.000003247695$$$A
$$$P{\left(X \lt 8 \right)} = 0.99999658647$$$A
$$$P{\left(X \leq 8 \right)} = 0.999999834165$$$A
$$$P{\left(X \gt 8 \right)} = 1.65835 \cdot 10^{-7}$$$A
$$$P{\left(X \geq 8 \right)} = 0.00000341353$$$A