# What are the mean and standard deviation of a probability density function given by Pr(X=k) = (14^ke^-14)/(k!)  for k in {0,1,2... oo}?

Nov 26, 2015

This is the Poisson distribution with $l a m \mathrm{da} = 14$

#### Explanation:

The mean and variance of the Poisson distribution is $l a m \mathrm{da}$

So for this problem ...

$\mu = {\sigma}^{2} = 14$

Standard Deviation $= \sqrt{l a m \mathrm{da}} = \sqrt{14}$

hope that helped