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A Poisson random variable is a variable X that takes on the integer values 0 ,...

A Poisson random variable is a variable X that takes on the integer values 0 , 1 , 2 , … with a probability mass function given by p ( i ) = P { X = i } = e − λ λ i i ! for i = 0 , 1 , 2 … , where the parameter λ > 0 .

A)Show that ∑ i p ( i ) = 1.

B) Show that the Poisson random variable can be used to approximate a binomial random variable when the binomial parameter n is large and p is small.

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