Question

If ' $m$ ' is the mean of a Poisson distribution, then $P(x>0)$ $=$

• A. $e^{-m}$
• B. $1-e^m$
• C. $\frac{e^m-1}{e^m}$
• D. $m^{-e}$

Answer 1

Answer: (C)

Mean of poisson distribution $=m$
Then, $P(X=x)=\frac{e^{-m}{m}^x}{x!},x=0,1,2,3,\dots$
$P(X>0)=1-P(X=0)$
$=1-\frac{e^{-m_{m}0}}{0!}=1-e^{-m}$
$=\frac{e^m-1}{e^{in}}$