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 = np

varience = npq

Mean - variance = np - npq

= np (1 - q)

= np.p

= np²

Mean - variance >0

Mean > variance

^{So, mean can never be less than variance.}

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