use poisson distribution to show that $e(x) = \\frac{1}{\\lambda}$ $var…

$use poisson distribution to show that $e(x) = \\frac{1}{\\lambda}$ $var…$

use poisson distribution to show that
$e(x) = \frac{1}{\lambda}$
$var(x) = \frac{1}{\lambda}$

For a Poisson distribution $X \sim \text{Poisson}(\lambda)$, the expected value and variance are:
$E(X) = \lambda$
$\text{Var}(X) = \lambda$