Problem 1 For an n E N, let X1, . .., Xn : S - R be either n discrete random variables with joint pmf P(X1 = 1, . .., Xn = "n) or n continuous random variables with joint pdf f ( 2 1 , . . . , an). (i) Furthermore, let a1, . .., an E R. Show that in either case (i.e. for discrete RVs on the one hand and for continuous RVs on the other hand), E (ii) Now assume that X1, ..., Xn are in addition independent. Show that in either case (i.e. for discrete RVs on the one hand and for continuous RVs on the other hand) , EX1 . . . . . Xn] = E[X]] . .. . . EXn]