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試行回数 $$$n = 10$$$、成功確率 $$$p = 0.175$$$ の二項分布に従う $$$P{\left(X = 1 \right)}$$$ を求めよ
入力内容
$$$n = 10$$$、$$$p = 0.175 = \frac{7}{40}$$$、$$$x = 1$$$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: $$$\mu = n p = \left(10\right)\cdot \left(\frac{7}{40}\right) = \frac{7}{4} = 1.75$$$A。
分散: $$$\sigma^{2} = n p \left(1 - p\right) = \left(10\right)\cdot \left(\frac{7}{40}\right)\cdot \left(1 - \frac{7}{40}\right) = \frac{231}{160} = 1.44375$$$A.
標準偏差: $$$\sigma = \sqrt{n p \left(1 - p\right)} = \sqrt{\left(10\right)\cdot \left(\frac{7}{40}\right)\cdot \left(1 - \frac{7}{40}\right)} = \frac{\sqrt{2310}}{40}\approx 1.201561484069792.$$$A
$$$P{\left(X = 1 \right)}\approx 0.309830084623023$$$A
$$$P{\left(X \lt 1 \right)}\approx 0.146062754179425$$$A
$$$P{\left(X \leq 1 \right)}\approx 0.455892838802448$$$A
$$$P{\left(X \gt 1 \right)}\approx 0.544107161197552$$$A
$$$P{\left(X \geq 1 \right)}\approx 0.853937245820575$$$A