Exercise: Iterated expectations

In this exercise, do not attempt formal mathematical derivations, which would actually involve some subtle issues when we go beyond discrete random variables. Rather, use your understanding of the concepts involved. For each one of the statements below, indicate whether it is true or false. (a) The law of iterated expectations tells us that E E [X | Y] ] = E [X]. Suppose that we want apply this law in a conditional universe, given another random variable Z, in order to evaluate E [X" | Z]. Then: E EX|Y, Z] | Z = E[X| Z] Select an option v EEXYZ] = EX|Z] Select an option v EEXY, Z] ] = E[X| Z] Select an option v (b) Determine whether each of the following statements about the quantity E g (X, Y) | Y, Z] is true or false. The quantity E g (X, Y) | Y, Z] is: a random variable Select an option v a number Select an option v . a function of (X, Y) Select an option v a function of (Y, Z) Select an option v . a function of Z only Select an option v