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Question
Can the mean of a binomial distribution be less than its variance?
Solution
No.
The mean of a binomial distribution is np and variance is npq.
If mean is less than its variance, then np <npq.
As both n and p are positive, we can divide both sides by np.
We get 1<q, which is not true as q <1 under all circumstances. (As p+q=1, q cannot be greater than 1)
So, the mean of a binomial distribution cannot be less than its variance.
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