Question

How do you determine the variance of a Poisson distribution?

Answer 1

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`) -`[E(X)]^2`.
if the random variable is a discrete random variable, we obtain
`sigma^2` = `sum_0^infty` `x^2`p(x) - `[ sum_0^inftyx.p(x)]^2` where
p(x) =`((e^(-mu}mu^x) / (x!))` x = 0,1,2,3,-----`infty`
Finally, the answer is obtained as `mu`.