Earlier this semester we learned that if X, Y and Z are random variables and a, b, and c are constants, then the variance of (aX + bY + cZ) = a² var(X) + b² var(Y) + c² var(Z) + 2ab cov(X,Y) + 2ac cov(X,Z) + 2bc cov(Y,Z). Using the algebra of expectations operators (hint: remember from Lecture 2 we said “the variance of ANYTHING can be calculated this way….”, prove this is true. Show all your work. (15 marks)