对于参数为 $$$n = 7$$$ 和 $$$p = 0.1$$$ 的二项分布，求 $$$P{\left(X = 1 \right)}$$$

根据 $$$n = 7$$$、$$$p = 0.1 = \frac{1}{10}$$$ 和 $$$x = 1$$$ 计算二项分布的各项数值。

平均值：$$$\mu = n p = \left(7\right)\cdot \left(\frac{1}{10}\right) = \frac{7}{10} = 0.7$$$A。

方差：$$$\sigma^{2} = n p \left(1 - p\right) = \left(7\right)\cdot \left(\frac{1}{10}\right)\cdot \left(1 - \frac{1}{10}\right) = \frac{63}{100} = 0.63$$$A。

标准差: $$$\sigma = \sqrt{n p \left(1 - p\right)} = \sqrt{\left(7\right)\cdot \left(\frac{1}{10}\right)\cdot \left(1 - \frac{1}{10}\right)} = \frac{3 \sqrt{7}}{10}\approx 0.793725393319377.$$$A

$$$P{\left(X = 1 \right)} = 0.3720087$$$A

$$$P{\left(X \lt 1 \right)} = 0.4782969$$$A

$$$P{\left(X \leq 1 \right)} = 0.8503056$$$A

$$$P{\left(X \gt 1 \right)} = 0.1496944$$$A

$$$P{\left(X \geq 1 \right)} = 0.5217031$$$A