If XXX and YYY are independent and X,Y∼Exp(λ)X, Y \sim \text{Exp}(\lambda)X,Y∼Exp(λ), what is the distribution of Z=X+YZ = X + YZ=X+Y?
Exponential with rate λ/2\lambda/2λ/2
Erlang with shape 2 and rate λ\lambdaλ
Poisson with mean 2/λ2/\lambda2/λ
Normal with mean 2/λ2/\lambda2/λ