Let X∼Beta(α,β)X \sim \text{Beta}(\alpha, \beta)X∼Beta(α,β). What is the variance?
αβ(α+β)2(α+β+1)\frac{\alpha\beta}{(\alpha+\beta)^2(\alpha+\beta+1)}(α+β)2(α+β+1)αβ
α(α+β)2\frac{\alpha}{(\alpha+\beta)^2}(α+β)2α
αβα+β\frac{\alpha\beta}{\alpha+\beta}α+βαβ
1α+β\frac{1}{\alpha+\beta}α+β1