Problem 1 The definition of variance for random variable is as follows Var[X] = B[X – B[X]1? = B[X2] - (E[x])? 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] = B[X²]E[Y?] – (E[X])}E[Y])?. 3. (10 %) Furthermore, if B[X] = 0, Var[XY] = Var[X]B[Y?). = Hint: B[XY] = B[X]E[Y] if X and Y are independent random variables.