Question

Suppose x₁ ∼ exp(λ₁), x₂ ∼ exp(λ₂), ..., xₙ ∼ exp(λₙ) and all are independent. Let T = min(x₁, x₂, ..., xₙ). Show that T ∼ exp(λ₁ + λ₂ + ... + λₙ).