2. Recall that the covariance between two random variables X and Y is defined as cov (X, Y) = EH(X - E(X)HY - E(Y)}. This should be covered in your prerequisites, but you can also refer to the Wikipedia page at: https://en. wikipedia. org/wiki/Covariance (a) Prove that cov(X, Y) = E(XY) - E(X) E(Y). (b) Let Z be another random variable, prove that cov(X + Y, Z) = cov(X, Z) + cov ( Y, Z). (c) Now consider the situation with two sequences of random variables X1, . .., Xm and Y1, ..., Yn. Prove that m COV S cov(X;, Y;), j = 1, ..., n, and use it to prove that n COV Ex. EY, = EE cov (X;, Y;). j=1 i-1 j=1