# What are the mean and standard deviation of a probability density function given by Pr(X=k) = (18^ke^-18)/(k!)  for k in {0,1,2... oo}?

Dec 23, 2015

This is the Poisson distribution with $l a m \mathrm{da} = 18$

#### Explanation:

The mean and variance of the Poisson distribution are both equal to $l a m \mathrm{da}$

$\mu = l a m \mathrm{da} = 18$
$\sigma = \sqrt{l a m \mathrm{da}} = \sqrt{18} = 3 \sqrt{2} \approx 4.243$

hope that helped