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Binomial Distribution — Maths STD 12 Science — Question

Gujarat 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 = np varience = npq Mean - variance $= np - npq = np (1 - q) = np.$
$p = np^2$ Mean - variance > 0 Mean > variance
So, mean can never be less than variance.

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