对于参数为 $$$n = 30$$$ 和 $$$p = 0.5$$$ 的二项分布，求 $$$P{\left(X = 0 \right)}$$$

根据 $$$n = 30$$$、$$$p = 0.5 = \frac{1}{2}$$$ 和 $$$x = 0$$$ 计算二项分布的各项数值。

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

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

标准差: $$$\sigma = \sqrt{n p \left(1 - p\right)} = \sqrt{\left(30\right)\cdot \left(\frac{1}{2}\right)\cdot \left(1 - \frac{1}{2}\right)} = \frac{\sqrt{30}}{2}\approx 2.738612787525831.$$$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