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If X is Binomial distributed with mean 2 and variance 4/3 ,find the probability distribution of X.
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We have E(X) = np = 2, v(x) = npq = $\frac{4}{3}$

$ ∴ \frac{npq}{np} = \frac{(\frac{4}{3})}{2} = \frac{2}{3} $

$ ∴ q = \frac{2}{3} ∴ p = 1- \frac{2}{3} = \frac{1}{3} $

∵ np = 2 ∴ n.$\frac{1}{3}$ = 2 or n = 6

The distribution is p(X=x) = $^nC_x p^x q^{n-x} = (^6C_x) (\frac{2}{3})^x (\frac{1}{3})^{6-x}$

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