1. If X1, . .., Xn are random variables and Y := _. aiXi, where di E R for all i = 1, ..., n. Similar to E(X1 + X2) = E(X1) + E(X2) and E(aX + b) = a E(X) + b, we have E(Y) = a; E(Xi ). Show that Var(Y) = a? Var(Xi) + 2 ) aia; Cov ( Xi, X;), where the summation extends over all values of i and j from 1 to n for which i