Consider nnn i.i.d. variables Xi∼Exponential(λ)X_i \sim \text{Exponential}(\lambda)Xi∼Exponential(λ). What is the distribution of S=∑i=1nXiS = \sum_{i=1}^n X_iS=∑i=1nXi?
Gamma(n,λ)\text{Gamma}(n, \lambda)Gamma(n,λ)
Exponential(nλ)\text{Exponential}(n\lambda)Exponential(nλ)
Poisson(nλ)\text{Poisson}(n\lambda)Poisson(nλ)
χ2(2n)\chi^2(2n)χ2(2n)