Q. For a poisson variate $X$, if $P(X = 2) = 3P(X = 3)$, then the mean of $X$ is
A) 1
B) $\frac{1}{2}$
C) $\frac{1}{3}$
D) $\frac{1}{4}$
Explanation
(a)
Given, $P(X = k) = \frac{\lambda^{k}e^{- \lambda}}{k!}$
Since, $P(X = 2) = 3P(X = 3)$
$\Rightarrow \ \frac{\lambda^{2}e^{- \lambda}}{2!} = 3.\frac{\lambda^{3}e^{- \lambda}}{3!}\ \Rightarrow \ \lambda = 1$
$\therefore$ Mean of poisson distribution is 1
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.