Question: A random variable Z has Poisson distribution If for k = 0, 1, 2, . . . (a) Use the expansion to show that (b)

A random variable Z has Poisson distribution If
A random variable Z has Poisson distribution If for k =

for k = 0, 1, 2, . . .
(a) Use the expansion

A random variable Z has Poisson distribution If for k =

to show that

A random variable Z has Poisson distribution If for k =

(b) Calculate the mean E[Z] and the variance V(X).

p(k) = P (Z < k) k! 2 3 2 3!

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