Consider four random variables X1; X2; X3; X4. Let E(X1) = 20, E(X2) = 30, E(X3) = 40 and E(X4) = 60. Assume that their variances are all equal with 4: Var(X1) = Var(X2) = Var(X3) = Var(X4) = 4. Define the random variable L = X1 + X2 + X3 + X4. 1. Find the mean and the variance of L if X1; X2; X3; X4 are uncorrelated. 2. Find the mean and the variance of L if the correlation between any two of X1; X2; X3; X4 is 0:2, i.e. Corr(X_j; X_k) = 0:2 if 1 <= j < k <= 4.

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