# 3 a 2 pts For XPois find EX the average factoria.pdf

A

3. (a) (2 pts) For XPois(), find E[X!] (the average factorial of X ), if it is finite. (b) (2 pts: Sum of independent Poissons: convolution property) Use the Law of total probability to show that if XPois( 1),YPois(2), and X is independent of Y, then X+Y Pois(1+2).

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### 3 a 2 pts For XPois find EX the average factoria.pdf

• 1. 3. (a) (2 pts) For XPois(), find E[X!] (the average factorial of X ), if it is finite. (b) (2 pts: Sum of independent Poissons: convolution property) Use the Law of total probability to show that if XPois( 1),YPois(2), and X is independent of Y, then X+Y Pois(1+2)
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