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If the mean and variance of a binomial distribution are respectively 9 and 6, find the distribution.
Let X denote the variance with parameters n and p
p + q = 1 ⇒ q = 1 - p
Given, mean = np = 9 and variance = npq = 6
npq = 6
⇒9q = 6
Now, np = 9
⇒ n = 27
The required binomial distribution is given by,