# What are the mean and standard deviation of a probability density function given by Pr(X=k) = (12^ke^-12)/(k!)  for k in {0,1,2... oo}?

mean $\lambda = 12$
standard deviation $\sqrt{\lambda} = \sqrt{12} = 3.464$

#### Explanation:

Probability of events for a Poisson distribution
An event can occur 0, 1, 2, … times in an interval. The average number of events in an interval is designated $\lambda$. $\lambda$ is the event rate, also called the rate parameter. The probability of observing $k$ events in an interval is given by the equation

P("k events in interval") = (lambda^k e^(-lambda))/(k!)

The mean is equal to the variance

mean $= \lambda = {\sigma}^{2}$
and standard deviation $\sigma = \sqrt{\lambda}$

God bless....I hope the explanation is useful.