Q34Single correct3 Marks16 Jul 2023

Let $X\sim\operatorname{Binomial}(n,p)$. If the expected value and variance of $X$ are $2$ and $\frac{3}{2}$ respectively, find the value of $P(X=2)$.

A

$\frac{7\times 3^6}{4^7}$

B

$\frac{7\times 3^6}{4^8}$

C

$\binom{8}{2}\times\frac{3^2}{4^8}$

D

$\binom{4}{2}\times\frac{3^2}{4^4}$