Q. 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) $\frac{1}{e^{2}}$
Explanation
(c)
Given $P(X = 1) = P(X = 2)$
$\therefore\ \frac{e^{- \lambda}\lambda^{1}}{1!} = \frac{e^{- \lambda}\lambda^{2}}{2!}\ \Rightarrow \ \lambda = 2$
$\therefore\ P(X = 4) = \frac{e^{- 2}(2)^{4}}{4!} = \frac{2}{3e^{2}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.