If X∼Gamma(α,β)X \sim \text{Gamma}(\alpha, \beta)X∼Gamma(α,β) with PDF βαΓ(α)xα−1e−βx\frac{\beta^\alpha}{\Gamma(\alpha)} x^{\alpha-1} e^{-\beta x}Γ(α)βαxα−1e−βx, what is the mode of the distribution for α>1\alpha > 1α>1?
α−1β\frac{\alpha-1}{\beta}βα−1
αβ\frac{\alpha}{\beta}βα
α+1β\frac{\alpha+1}{\beta}βα+1
β(α−1)\beta(\alpha-1)β(α−1)