2.11 Let X and Y be independently distributed according to distributions P and Q, respectively. Suppose that

2.11 Let X and Y be independently distributed according to distributions Pξ and Qη, respectively. Suppose that ξ and η are real-valued and independent according to some prior distributions  and 

. If, with squared error loss, δ is the Bayes estimator of ξ

on the basis of X, and δ

 is that of η on the basis of Y ,

(a) show that δ

 − δ is the Bayes estimator of η − ξ on the basis of (X, Y );

(b) if η > 0 and δ∗

 is the Bayes estimator of 1/η on the basis of Y , show that δ · δ∗



is the Bayes estimator of ξ/η on the basis of (X, Y ).