Consider the following loss function: L(theta,a)={[c_(1)(theta-a),a theta]:} (a) Find an expression for the Bayes estimator of theta.

Consider the following loss function: L(theta,a)={[c_(1)(theta-a),a <= theta],[c_(2)(a-theta),a > theta]:} (a) Find an expression for the Bayes estimator of theta. (b) What is the Bayes estimator of theta if c_(1)=c_(2) ? (c) What is the Bayes estimator of theta if c_(2)=1-c_(1), where c_(1) < 1 ? 2. Consider the following loss function: L(theta,a)=(a)/( theta)-log((a)/( theta))-1 (a) Find a general expression for the Bayes estimator of theta. (b) Suppose Y_(i)thetaPo(theta),i=1,dots,n, with prior distribution thetaGamma(a,b). Find the Bayes estimator for theta in this case. 3. Consider the loss function L(theta,a)=exp{c(a-theta)}-c(a-theta)-1 (a) Show that a Bayes estimator of theta under this loss is given by -(1)/(c)log(E[e^(-c theta)y]) (b) Suppose Y