Consider two independent random variables X∼Exp(λ)X \sim \text{Exp}(\lambda)X∼Exp(λ) and Y∼Exp(λ)Y \sim \text{Exp}(\lambda)Y∼Exp(λ). What is the PDF of Z=X−YZ = X - YZ=X−Y?
\frac{\lambda}{2} e^{-\lambda |z|}
\lambda e^{-\lambda |z|}
\frac{1}{2} e^{-\lambda z}
\lambda^2 e^{-\lambda z}