Question

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

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

Answer 1

Answer: (C)

Given that, $P(X-1) = P(X=2)$
$\frac{e^{-\lambda} \lambda^{1}}{1 !}=\frac{e^{-\lambda} \lambda^{2}}{2 !} \Rightarrow \lambda=2$
$\therefore P(X=4)=\frac{e^{-2}(2)^{4}}{4 !}=\frac{e^{-2} \times 16}{24}=\frac{2}{3 e^{2}}$