Question

What are the mean and standard deviation of a binomial probability distribution with `n=2` and `p=4/17`?

Answer 1

The mean is `mu=n*p=2* 4/17=8/17 approx 0.4706` and the standard deviation is `sigma=sqrt{n*p*(1-p)}=sqrt{2*4/17*13/17}=sqrt{104/289} approx 0.5999`

Explanation:

The special formulas `mu=n*p` and `sigma=sqrt{n*p*(1-p)}` only work for binomial random variables, where `n` is the number of independent trials with outcomes "success" or "failure", and `p` is the probability of "success" on each trial. The random variable `X` itself counts the number of successes in `n` trials.