The definition of variance for random variable is as follows

Problem 1 The definition of variance for random variable is as follows Var[X] = E[X - E[X]]' = E[X'] - (FIX]). Assume that X and Y are independent random variables, verify thee following properties: 1. (10 %) Var[X + Y] = Var[X] + Var[Y]. 2. (10 %) Var[XY] = E[X3 JE[Y2 ] - (E[XD) (BLYD)2. 3. (10 %) Furthermore, if E[X] = 0, Var[XY] = Var[X]IE[Y2]. Hint: E[XY] = E[X]E[Y] if X and Y are independent random variables