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Distributionseasy
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Consider two independent random variables X∼Poisson(λ1=2)X \sim \text{Poisson}(\lambda_1 = 2)X∼Poisson(λ1​=2) and Y∼Poisson(λ2=3)Y \sim \text{Poisson}(\lambda_2 = 3)Y∼Poisson(λ2​=3). What is the distribution of Z=X+YZ = X + YZ=X+Y?