This problem considers the Poisson distribution, a probability distribution for a discrete random variable which was first used by Simeon-Denis Poisson to describe seemingly random criminal events in 1837 in Paris. If independent events have a constant tendency to occur and if the average rate of occurrence is a, then the probability that n events actually occur is given by
(a) By noting that
thereby verifying that the poisson distribution is normalized.
I've done this already
(b) By using and , show that
thereby verifying that the average rate of occurrence, or the expectation value , is equal to a.
I've done this one as well
(c) By using similar techniques, find and show, using and
that the standard deviation of the poisson distribution is given by
This is the one I need help with