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Binomial Distribution — MATHS STD 12 Science — Question

Rajasthan 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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