X and Y are random variables with E X E Y 0 suce that X has standard deviation x 2 while Y has standard deviation Y 4 (a) For V X Y, What are the smallest and largest possible values of Var V (b) For w X 2Y, what are the smallest and largest possible values of Var W ...

a Since EV EX EY 0 VarV E V 2 E X 2 2XY Y 2 VarX VarY ...

X and Y are random variables with E[X] = E[Y] = 0 suce that X has standard

Question:

X and Y are random variables with E[X] = E[Y] = 0 suce that X has standard deviation σx = 2 while Y has standard deviation σY = 4.
(a) For V = X - Y, What are the smallest and largest possible values of Var[V]?
(b) For w = X - 2Y, what are the smallest and largest possible values of Var[W]?