Question

If $X$ is a Poisson variate such that $P(X=1)=P(X=2)$ then $P(X=4)=$

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

Answer 1

Answer: (C)

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

$P(x;\mu )=\frac{e^{-\mu }{\mu }^x}{x!}$
$P(X=1)=P(X=2)$

$\frac{e^{-\mu }{\mu }^1}{1!}=\frac{e^{-\mu }{\mu }^2}{2!}$

$\mu =2$
$P(X=4)=\frac{e^{-2}{2}^4}{4!}=\frac{2}{3e^2}$