Let X∼Gamma(α,1)X \sim \text{Gamma}(\alpha, 1)X∼Gamma(α,1). What is the distribution of Y=1XY = \frac{1}{X}Y=X1?
Inverse-Gamma (α,1)(\alpha, 1)(α,1)
Gamma (1/α,1)(1/\alpha, 1)(1/α,1)
Beta (α,1)(\alpha, 1)(α,1)
Exponential (α)(\alpha)(α)