8.5 Let X1,...,Xn be independent, positive variables, each with density (1/ )f (xi/ ), and let ...

8.5 Let X1,...,Xn be independent, positive variables, each with density (1/τ )f (xi/τ ), and let τ have the improper density π(τ )=1/τ (τ > 0). The posterior density after one observation is a proper density, and it satisfies (B5), provided Eτ (1/X1) < ∞