对于参数为$$$n = 18$$$和$$$p = \frac{1}{8}$$$的几何分布，求$$$P{\left(X = 18 \right)}$$$

使用$$$n = 18$$$和$$$p = \frac{1}{8}$$$计算几何分布的各项数值（计入成功试次）。

平均值：$$$\mu = \frac{1}{p} = \frac{1}{\frac{1}{8}} = 8$$$A。

方差：$$$\sigma^{2} = \frac{1 - p}{p^{2}} = \frac{1 - \frac{1}{8}}{\left(\frac{1}{8}\right)^{2}} = 56$$$A。

标准差: $$$\sigma = \sqrt{\frac{1 - p}{p^{2}}} = \sqrt{\frac{1 - \frac{1}{8}}{\left(\frac{1}{8}\right)^{2}}} = 2 \sqrt{14}\approx 7.483314773547883.$$$A

$$$P{\left(X = 18 \right)}\approx 0.012913587642949$$$A

$$$P{\left(X \lt 18 \right)}\approx 0.896691298856407$$$A

$$$P{\left(X \leq 18 \right)}\approx 0.909604886499356$$$A

$$$P{\left(X \gt 18 \right)}\approx 0.090395113500644$$$A

$$$P{\left(X \geq 18 \right)}\approx 0.103308701143593$$$A