Consider X∼Beta(α,β)X \sim \text{Beta}(\alpha, \beta)X∼Beta(α,β). What is the coefficient of variation CV=σμCV = \frac{\sigma}{\mu}CV=μσ?
βα(α+β+1)\sqrt{\frac{\beta}{\alpha(\alpha+\beta+1)}}α(α+β+1)β
αβ(α+β+1)\sqrt{\frac{\alpha}{\beta(\alpha+\beta+1)}}β(α+β+1)α
α+β+1αβ\sqrt{\frac{\alpha+\beta+1}{\alpha \beta}}αβα+β+1
αβ\sqrt{\frac{\alpha}{\beta}}βα