Question

What are the mean and standard deviation of a binomial probability distribution with `n=18` and `p=2/32`?

Answer 1

The mean is `mu=n * p=18 * 1/16 = 9/8` and the standard deviation is `sigma=sqrt{n * p * (1-p)}=sqrt{135/128}=(3sqrt[15})/(8sqrt{2})=(3sqrt{30})/16 approx 1.027`

Explanation:

A binomial random variable `X` counts the number of successes in `n` trials, when each trial is independent from the others with a constant probability `p` of success.

The mean of `X` is `mu=n * p` and the standard deviation of `X` is `sigma=sqrt{n * p * (1-p)}`.