Q. If $X$ is a poisson variate with $P(X = 0) = 0.8,$ then the variance of $X$ is
A) $\log_{e}20$
B) $\log_{10}20$
C) $\log_{e}\frac{5}{4}$
D) 0
Explanation
(c)
Given, $P(X) = \frac{e^{- m}m^{x}}{x!}$
$\therefore\ P(X = 0) = \frac{e^{- m}1}{1}$
$\Rightarrow \ 0.8 = e^{- m}\ \Rightarrow \ - m\log_{e}{0.8}$
$\Rightarrow \ \ m = \log_{e}{\frac{10}{8} = \log_{e}\frac{5}{4}}$
$\therefore$ Variance $= m = \log_{e}\frac{5}{4}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.