"Let X be a random variable having binomial distribution B(7, p). If P(X = 3) = 5P(x = 4), then the sum of the mean and the variance of X is :"

Question

Accepted Answer

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Given P(X = 3) = 5P(X = 4) and n = 7

$\Rightarrow {}^7{C_3}{p^3}{q^4} = 5\,.\, \Rightarrow {}^7{C_4}{p^4}{q^3}$

$\Rightarrow q = 5p$ and also $p + q = 1$

$\Rightarrow p = {1 \over 6}$ and $q = {5 \over 6}$

Mean $= {7 \over 6}$ and variance $= {{35} \over {36}}$

Mean + Variance $= {7 \over 6} + {{35} \over {36}} = {{77} \over {36}}$

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Let X be a random variable having binomial distribution B(7, p). If P(X = 3) = 5P(x = 4), then the sum of the mean and the variance of X is :