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Find $$$P{\left(X = 1 \right)}$$$ for binomial distribution with $$$n = 10$$$ and $$$p = 0.1$$$
Your Input
Calculate the various values for the binomial distribution with $$$n = 10$$$, $$$p = 0.1 = \frac{1}{10}$$$, and $$$x = 1$$$.
Answer
Mean: $$$\mu = n p = \left(10\right)\cdot \left(\frac{1}{10}\right) = 1$$$A.
Variance: $$$\sigma^{2} = n p \left(1 - p\right) = \left(10\right)\cdot \left(\frac{1}{10}\right)\cdot \left(1 - \frac{1}{10}\right) = \frac{9}{10} = 0.9$$$A.
Standard deviation: $$$\sigma = \sqrt{n p \left(1 - p\right)} = \sqrt{\left(10\right)\cdot \left(\frac{1}{10}\right)\cdot \left(1 - \frac{1}{10}\right)} = \frac{3 \sqrt{10}}{10}\approx 0.948683298050514.$$$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