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.
What will be an ideal response?
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;
Computer Science & Information Technology
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