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

Question

Philoid · Accepted Answer

Let X be a binomial variate with parameters in and p.

Mean = np

Variance = npq

Mean - Variance = np – npq

= np(1 - q)

= np² > 0

So, Mean – Variance > 0

⇒ Mean >Variance

So, mean can never be less than variance.