Let GF be a -algebra and X,YL1(,F,P). Recall and use the definition of conditional expectation from Definition 2.1 in the lecture to show the following properties: (a) For R we have E[X+YG]=E[XG]+E[YG]; (b) If XY, then E[XG]E[YG]; (c) If (X) and G are independent, then E[XG]=E[X]