对于参数为 $$$n = 10$$$ 和 $$$p = 0.1$$$ 的二项分布，求 $$$P{\left(X = 1 \right)}$$$

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

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

方差：$$$\sigma^{2} = n p \left(1 - p\right) = \left(10\right)\cdot \left(\frac{1}{10}\right)\cdot \left(1 - \frac{1}{10}\right) = \frac{9}{10} = 0.9$$$A。

标准差: $$$\sigma = \sqrt{n p \left(1 - p\right)} = \sqrt{\left(10\right)\cdot \left(\frac{1}{10}\right)\cdot \left(1 - \frac{1}{10}\right)} = \frac{3 \sqrt{10}}{10}\approx 0.948683298050514.$$$A

$$$P{\left(X = 1 \right)} = 0.387420489$$$A

$$$P{\left(X \lt 1 \right)} = 0.3486784401$$$A

$$$P{\left(X \leq 1 \right)} = 0.7360989291$$$A

$$$P{\left(X \gt 1 \right)} = 0.2639010709$$$A

$$$P{\left(X \geq 1 \right)} = 0.6513215599$$$A