Can the mean of a binomial distribution be less than its variance… - Vidyadip

Question

Can the mean of a binomial distribution be less than its variance?

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Answer

Let X be a binomial veriate with parameters n and p . Mean $=\mathrm{np}$ varience $=\mathrm{npq}$ Mean - variance $=\mathrm{np}-\mathrm{npq}=\mathrm{np}(1$ $-q)=n p . p=n p^2$ Mean - variance $>0$ Mean $>$ variance
So, mean can never be less than variance.

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