Consider the sum S=∑i=1nXiS = \sum_{i=1}^n X_iS=∑i=1nXi where Xi∼Exponential(λ)X_i \sim \text{Exponential}(\lambda)Xi∼Exponential(λ). What is the distribution of SSS?
Exponential(nλ)\text{Exponential}(n\lambda)Exponential(nλ)
Gamma(n,λ)\text{Gamma}(n, \lambda)Gamma(n,λ)
χ2(2n)\chi^2(2n)χ2(2n)
Normal(n/λ,n/λ2)\text{Normal}(n/\lambda, n/\lambda^2)Normal(n/λ,n/λ2)