If 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) are independent, what is the distribution of X+YX+YX+Y?
Poisson(λ1+λ2)\text{Poisson}(\lambda_1 + \lambda_2)Poisson(λ1+λ2)
Poisson(λ1λ2)\text{Poisson}(\lambda_1 \lambda_2)Poisson(λ1λ2)
Normal(λ1,λ2)\text{Normal}(\lambda_1, \lambda_2)Normal(λ1,λ2)
Negative Binomial(λ1,λ2)\text{Negative Binomial}(\lambda_1, \lambda_2)Negative Binomial(λ1,λ2)