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In a binomial distribution B(n, p), the sum and product of the mean & variance are 5 and 6 respectively, then find $$6(n + p - q)$$ is equal to :-
Let mean $$M = np$$ and variance $$V = npq$$.
$$M + V = 5$$
$$M \cdot V = 6$$
Since variance must be less than the mean ($$V < M$$): $$V = 2, \quad M = 3$$
$$npq = 2, \quad np = 3$$
$$q = \frac{npq}{np} = \frac{2}{3}$$
$$p = 1 - \frac{2}{3} = \frac{1}{3}$$
$$n\left(\frac{1}{3}\right) = 3 \implies n = 9$$
$$6(n + p - q) = 2 \times 26 = 52$$
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