Let X∼Exp(λ)X \sim \text{Exp}(\lambda)X∼Exp(λ). What is the distribution of Y=min(X1,X2,…,Xn)Y = \min(X_1, X_2, \dots, X_n)Y=min(X1,X2,…,Xn) where XiX_iXi are i.i.d.?
Exp(nλ)\text{Exp}(n\lambda)Exp(nλ)
Exp(λ/n)\text{Exp}(\lambda/n)Exp(λ/n)
Exp(λn)\text{Exp}(\lambda^n)Exp(λn)
Gamma(n,λ)\text{Gamma}(n, \lambda)Gamma(n,λ)