Given X∼Gamma(α,β)X \sim \text{Gamma}(\alpha, \beta)X∼Gamma(α,β), what is the distribution of Y=cXY = cXY=cX?
Gamma(α,β)\text{Gamma}(\alpha, \beta)Gamma(α,β)
Gamma(α,β/c)\text{Gamma}(\alpha, \beta/c)Gamma(α,β/c)
Gamma(α,cβ)\text{Gamma}(\alpha, c\beta)Gamma(α,cβ)
Gamma(cα,β)\text{Gamma}(c\alpha, \beta)Gamma(cα,β)