Answer to Question #125957 in Statistics and Probability for muhammad Adnan

Question

This problem considers the Poisson distribution, a probability distribution for a discrete random variable which was first used by SimeÂon-Denis Poisson to describe seemingly random criminal events in Paris in 1837. 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 pn ?? eÿaan n! with n ?? 0, 1, 2,. . . 1:

Answer 1

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

P_n = $\frac {e^{-a} •\ a^{n}}{n!}$

where n= 0,1,2,3......

And

$\sum_{n=0}^{+\infty} P_n \\$ = 1