Define the covariance of two random variables X and Y to be Cov(X, Y) = EXY]- EX]EY]. (a) Check that Cov(X, X) = Var(X), that Cov(X, Y) = Cov(Y, X), and that Cov(., .) is a bilinear function of its arguments. That is, if one fixes one ar- gument (one of the independent variables; X or Y in the definition above) then it is a linear function of the other. For example, if we fix the sec- ond argument, then for real constants a and b we have Cov(aX + bY, Z) = aCov(X, Z) + bCov(Y, Z). (b) If Cov(Xi, Xj) = ouj, find Cov(X1 - X2, X3 -2X4) in terms of the ouj. (c) If Cov(Xi, Xj) = ouj, find Var(X1 + 2X2 + 3X3) in terms of the ouj