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Sum of independent Poissons

MediumProbabilityRandom Variables~4m

X∼Poisson(3)X\sim\text{Poisson}(3) and Y∼Poisson(5)Y\sim\text{Poisson}(5) are independent. What is P(X+Y=2)P(X+Y = 2)? (to 4 decimals)

Show hints (2)+
  1. First show X+Y ~ Poisson(3+5) via multiplying generating functions.
  2. Then evaluate e^(−8)·8²/2!.

Answer

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0.0107 (± 0.0005)

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