# How do you determine the variance of a Poisson distribution?

Nov 8, 2015

The Poisson Distribution is that of a discrete random variable. Hence we use the summation procedure.

#### Explanation:

For any random variable X, the variance is defined as

${\sigma}^{2}$ = E(${X}^{2}$) -${\left[E \left(X\right)\right]}^{2}$.
if the random variable is a discrete random variable, we obtain
${\sigma}^{2}$ = ${\sum}_{0}^{\infty}$${x}^{2}$p(x) - ${\left[{\sum}_{0}^{\infty} x . p \left(x\right)\right]}^{2}$ where
p(x) =((e^(-mu}mu^x) / (x!))  x = 0,1,2,3,-----$\infty$
Finally, the answer is obtained as $\mu$.