Question 396 of 417MediumMCQ
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 :
Solutions · 1
Official solution
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 \[ = {7 \over 6} + {{35} \over {36}} = {{77} \over {36}}\] Answer the question to unlock