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