Let X 1 , X 2 , , Xn be independent random variables with Xi Exponential(). Define Y = X 1 +X 2 ++X

Let X₁, X₂, ⋯, Xn be independent random variables with Xi ∼ Exponential(λ). Define Y = X₁ +X₂ +⋯+X_n.

As we will see later, Y has a Gamma distribution with parameters n and λ, i.e., Y ∼ Gamma(n,λ). Using this, show that if Y ∼ Gamma(n,λ), then EY = n/λ and V ar(Y ) = n/λ².