幾何分佈計算器

計算給定 $$$n = 7$$$ 與 $$$p = 0.5 = \frac{1}{2}$$$ 的幾何分布各種數值（包含成功試驗）。

平均值：$$$\mu = \frac{1}{p} = \frac{1}{\frac{1}{2}} = 2$$$A。

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

標準差：$$$\sigma = \sqrt{\frac{1 - p}{p^{2}}} = \sqrt{\frac{1 - \frac{1}{2}}{\left(\frac{1}{2}\right)^{2}}} = \sqrt{2}\approx 1.414213562373095$$$A。

$$$P{\left(X = 7 \right)} = 0.0078125$$$A

$$$P{\left(X \lt 7 \right)} = 0.984375$$$A

$$$P{\left(X \leq 7 \right)} = 0.9921875$$$A

$$$P{\left(X \gt 7 \right)} = 0.0078125$$$A

$$$P{\left(X \geq 7 \right)} = 0.015625$$$A