2. In this exercise, you will show that the is a weighted average of 4 and 4 as stated in class (assuming all variables are positive). A weighted average of two positive numbers X and Y is given by aX + (1 - a)Y for some fraction a between 0 and 1 (if a= 1/2, this is just a plain average). (a) Show that a weighted average of two numbers X and Y must lie between X and Y. (Hint: one number has to be larger than the other, so let X