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