Let X be a binomial random variable with mean N p and variance N p(1?p). Show that the ratio X/N also has a binomial distribution with mean p and variance p(1 ? p)/N.

Question

What will be an ideal response?

Answer 1

Let r = X/N. Since X has a binomial distribution, r also has the

same distribution. The mean and variance for r can be computed as follows:

Mean, E[r] = E[X/N] = E[X]/N = (N p)/N = p;