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)

$\frac{2}{3e^{2}}$

Answer 2

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