Question

If X has Poisson distribution with parameter $m=1$, find $P[X\le 1]$. (Use $e^{-1}=0.3679$)

Answer 1

We have Poisson distribution,

$P\left(r\right)=\frac{e^{-m}{m}^r}{r!}$

Here, $m=1$

$\therefore P(X\le 1)=P\left(0\right)+P\left(1\right)$

$=\frac{e^{-1}{\left(1\right)}^0}{0!}+\frac{e^{-1}{\left(1\right)}^1}{1!}$

$=e^{-1}+e^{-1}$

$=2.e^{-1}$

$=2\left(0.3679\right)$ (as $e^{-1}=0.3679$)

$0.7358$

Answer is $0.7358$