Let X∼Gamma(α,β)X \sim \text{Gamma}(\alpha, \beta)X∼Gamma(α,β) with PDF f(x)=βαΓ(α)xα−1e−βxf(x) = \frac{\beta^\alpha}{\Gamma(\alpha)} x^{\alpha-1} e^{-\beta x}f(x)=Γ(α)βαxα−1e−βx. What is the mode for α>1\alpha > 1α>1?
(α−1)/β(\alpha-1)/\beta(α−1)/β
αβ\alpha\betaαβ
β/α\beta/\alphaβ/α
α/β\alpha/\betaα/β