WCC blackboard • WCC Gateway DH 2019 Cust Suppose that X and Y are independent continuous random variables. Show that oxy = 0. olf X and Y are independant, then fxx (x, y) = fx (x) –fy (y) and the range of (X, Y) is rectangular. Therefore, E (XY) = = S xy (x ) – dxdy = Sofa() ix- / xx ()dy = E(X) = E(Y) Hence, OXY = 0 O if X and Y are independant, then fxy (x,y) = fx (x) +fy(y) and the range of (X, Y) is rectangular. Therefore, E (XY) = | xy (xy ((8) +fy () dxdy = { xfkle = *(x)dx+ / wy()dy = E(X) + EN Hence, OXY = 0 If X and Y are independant, then fxr (x, y) = fx (x)fr (y) and the range of (X,Y) is rectangular. Therefore, E (XY) = | xvfx (W)fy ©) dxiy = /vfx (x)dix / xtz (b)dx= E(X) E (N) Hence, OXY = 0 olf X and Y are independant, then fxx (x,y) = fx (x)/x (y) and the range of (X,Y) is rectangular. Therefore, E (XY) = fx (0)5y (6) dxiy = [5x(x) dx [5x()ay = E(X) E (1) Hence, OXY = 0 O and the range of (X,Y) is rectangular. Therefore, If X and Y are independant, then fxx (x, y) = fx (x) Jxyfx (x) dx ?? -dxdy = Sfy (x) dx Hence, Oxy = 0 EXY) = // E(X) E(Y) Type here to search o ? ? g