Q6Single correct3 Marks13 Jul 2025

Let $X_1,X_2$ and $X_3$ be three independent and identically distributed Poisson random variables with mean $\lambda=3$. Find the probability that exactly one of the $X_i$ is equal to $0$, and the other two variables are greater than $1$.

A

$3e^{-3}(1-4e^{-3})^2$

B

$6e^{-3}(1-4e^{-3})$

C

$e^{-3}(1-4e^{-3})^2$

D

$6e^{-6}(1-4e^{-3})^2$