## Question

###### Problem 1 [You can solve this problem nOW Let X,Y : S _ R be two (real-valued) continons random variables with joint pdfif 0 < y < 1 and - y < 1 < y elsefex;x) (T,y) =Calcnlate EIXYI; EIXI, and ElY|: Does ElXY| = Elx] - ElY hold? Are X and Y independent?Problem 2You can solve this problem after we discussed section 5.3 For â‚¬ NJ let X X, S + Rbe either n discrete random variables with joint pmf P(XI T14 Xn Tn) OT n continons random variables with joint pdf f(t1; Tn )Furthermore; le

Problem 1 [You can solve this problem nOW Let X,Y : S _ R be two (real-valued) continons random variables with joint pdf if 0 < y < 1 and - y < 1 < y else fex;x) (T,y) = Calcnlate EIXYI; EIXI, and ElY|: Does ElXY| = Elx] - ElY hold? Are X and Y independent? Problem 2 You can solve this problem after we discussed section 5.3 For â‚¬ NJ let X X, S + Rbe either n discrete random variables with joint pmf P(XI T14 Xn Tn) OT n continons random variables with joint pdf f(t1; Tn ) Furthermore; let Q1, - Gn â‚¬ R_ Show that in either case (i.e_ for discrete RVs on the one hand and for continons RVs on the other hand) , Ea;] a;EIX;] j=[ Now assume that Xn- Xn are in addition independent. Show that in either case (i.e. for discrete RVs on the one hand and for continous RVs on the other hand) , E[X X] = EIXi] EIX,]