Let X∼Beta(α,β)X \sim \text{Beta}(\alpha, \beta)X∼Beta(α,β). What is the mode of the distribution when α>1\alpha > 1α>1 and β>1\beta > 1β>1?
α−1α+β−2\frac{\alpha-1}{\alpha+\beta-2}α+β−2α−1
αα+β\frac{\alpha}{\alpha+\beta}α+βα
α−1α+β\frac{\alpha-1}{\alpha+\beta}α+βα−1
αα+β−2\frac{\alpha}{\alpha+\beta-2}α+β−2α