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Binomial Distribution — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsBinomial Distribution3 Marks
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 $=n p$ varience $=n p q$ Mean - variance $=n p-n p q=n p(1$ $-q)=n p . p=n p^2$ Mean - variance > $>0$ Mean > varianceSo, mean can never be less than variance.

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