Question

If $X$ is a poisson variate such that $P(X=1)=P(X=2)$, then $P(X=4)$ is equal to

• A. $\frac{1}{2e^2}$
• B. $\frac{1}{3e^2}$
• C. $\frac{2}{3e^2}$
• D. $\frac{1}{e^2}$

Answer 1

Answer: (C)

Given : $P(X=1)=P(X=2)$
$\frac{e^{-\lambda }}{1!}=\frac{e^{-\lambda }{\lambda }^2}{2!}$
$\Rightarrow \lambda =2$
$\therefore P\left(x=4\right)=\frac{e^{-2}{2}^4}{4!}=\frac{2}{3e^2}$