Let XXX and YYY be independent with X∼Poisson(λ1)X \sim \text{Poisson}(\lambda_1)X∼Poisson(λ1) and Y∼Poisson(λ2)Y \sim \text{Poisson}(\lambda_2)Y∼Poisson(λ2). What is the PMF of X+YX + YX+Y?
Poisson(λ1+λ2)(\lambda_1 + \lambda_2)(λ1+λ2)
Poisson(max(λ1,λ2))(\max(\lambda_1, \lambda_2))(max(λ1,λ2))
Binomial(λ1+λ2,0.5)(\lambda_1 + \lambda_2, 0.5)(λ1+λ2,0.5)
Negative Binomial