Let X1 depend on θ1 and X2 be independent of X1 and depend on θ2. Let θ1 and θ2 have independent prior distributions. Assume a squared-error loss. Let δ1 and δ2 be the Bayes estimators of θ1 and θ2 respectively

1) Show that δ1 - δ2 is the bayes estimator of θ1-θ2 given X = (X1, X2) and the setup described.

2) Now assume that θ2 > 0 (with probability 1), and let δ1 hat be the Bayes estimator of 1/θ2 under the setup above. Show that δ1δ2 hat is the bayes estimator of θ1/θ2 , given x = (X1, X2)