Question

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}`?

Answer 1

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.