Question: A random variable Z ahs Poisson distribution if p(k) = P(Z = ? k e ?k / k! For k = 0, 1, 2 .

A random variable Z ahs Poisson distribution if

p(k) = P(Z

= ?ke?k / k!

For k = 0, 1, 2 . . .

(a) Use the expansion

e = 1+A+ 2! +... 3!

To show that

image

(b) Calculate the mean E[Z] and the varianceVar(Z)

e = 1+A+ 2! +... 3!

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