試行回数 $$$n = 30$$$、成功確率 $$$p = 0.5$$$ の二項分布に従う $$$P{\left(X = 0 \right)}$$$ を求めよ

$$$n = 30$$$、$$$p = 0.5 = \frac{1}{2}$$$、$$$x = 0$$$を用いて二項分布のさまざまな値を計算します。

平均: $$$\mu = n p = \left(30\right)\cdot \left(\frac{1}{2}\right) = 15$$$A。

分散: $$$\sigma^{2} = n p \left(1 - p\right) = \left(30\right)\cdot \left(\frac{1}{2}\right)\cdot \left(1 - \frac{1}{2}\right) = \frac{15}{2} = 7.5$$$A.

標準偏差: $$$\sigma = \sqrt{n p \left(1 - p\right)} = \sqrt{\left(30\right)\cdot \left(\frac{1}{2}\right)\cdot \left(1 - \frac{1}{2}\right)} = \frac{\sqrt{30}}{2}\approx 2.738612787525831.$$$A

$$$P{\left(X = 0 \right)}\approx 9.31323 \cdot 10^{-10}$$$A

$$$P{\left(X \lt 0 \right)} = 0$$$A

$$$P{\left(X \leq 0 \right)}\approx 9.31323 \cdot 10^{-10}$$$A

$$$P{\left(X \gt 0 \right)}\approx 0.999999999068677$$$A

$$$P{\left(X \geq 0 \right)} = 1$$$A