Question

If $X$ is a Poisson variate with parameter $1.5$, then $P(X>1)$ is

• A. $1-e^{-1.5}$
• B. $e^{-1.5}\left(2.5\right)$
• C. $1-e^{-1.5}\left(2.5\right)$
• D. $1-e^{-1.5}\left(3.5\right)$

Answer 1

The correct option is C $1-e^{-1.5}\left(2.5\right)$

$P(X>1)$
$=1-\left[P\right(X=0)+P(X=1\left)\right]$
$=1-[e^{-1.5}+1.5e^{-1.5}]$
$=1-e^{1.5}(1+1.5)$
$=1-e^{1.5}\left(2.5\right)$