onsider a random vector X Rp and a random variable Y R. Let X and Y denote the supports of X and Y , respectively. (a) Consider the following problem of minimizing the weighted mean squared error over all pre- dictors: min f :X Y E[(X)(Y f (X))2], where : X (0, ) is a given weight function, which is positive valued. Find a solution to this minimization problem. Does the solution depend on the weight function ? (b) Consider the following problem of minimizing the weighted mean squared error over Rp: min Rp E[(X)(Y X)2]. Assume that E[(X)XX] is nonsingular. Find a solution to this minimization problem. Does the solution depend on the weight function