Question

For a binomial distribution, prove that the variance is less than the mean.

Answer 1

Let X be a binomial variate with parameters n and p. Then,

Mean = np

And, Variance = npq

Mean - Variance = np−npq=np(1−q)=np²

Mean−Variance>0     [n∈N,p>0,therefore,np²>0]

Mean>Variance