Let X∼Beta(α,β)X \sim \text{Beta}(\alpha, \beta)X∼Beta(α,β). What is the value of E[ln(X)]E[\ln(X)]E[ln(X)]?
ψ(α)−ψ(α+β)\psi(\alpha) - \psi(\alpha+\beta)ψ(α)−ψ(α+β)
ψ(α+β)−ψ(α)\psi(\alpha+\beta) - \psi(\alpha)ψ(α+β)−ψ(α)
ψ(α)−ψ(β)\psi(\alpha) - \psi(\beta)ψ(α)−ψ(β)
ln(αα+β)\ln(\frac{\alpha}{\alpha+\beta})ln(α+βα)