Let X∼Beta(α=2,β=2)X \sim \text{Beta}(\alpha=2, \beta=2)X∼Beta(α=2,β=2). What is the Fisher Information I(α)I(\alpha)I(α)?
ψ′(α)−ψ′(α+β)\psi'(\alpha) - \psi'(\alpha+\beta)ψ′(α)−ψ′(α+β)
ψ′(α)+ψ′(β)\psi'(\alpha) + \psi'(\beta)ψ′(α)+ψ′(β)
ψ′(α+β)\psi'(\alpha+\beta)ψ′(α+β)
1/α21/\alpha^21/α2