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