Let X have a Pareto distribution with parameters Λ and θ. Let Λ have a gamma distribution with parameters α and 1 (i.e., scale parameter = 1). Find the unconditional pdf of X.
I tried finding the unconditional pdf of X by:
I'm stuck at the integral evaluation. Can I and how do I modify the integrand on the RHS to a density function such that direct integration is avoided in this case?