1. Covariance?!?! [15 points] autograded Recall the 'Hungry Washing Machine' question from section. You have 10 pairs of socks, where each is a different color. Left and right socks are distinct. Your washing machine randomly eats 4 socks. Suppose that your washing machine is equally likely to eat any 4 of your 20 distinct socks. For i = 1, . . . , 10, let Xi be the indicator/Bernoulli random variable that is 1 if pair i is complete after this fiasco and 0 otherwise. Let Y = P10 i=1 Xi be the total number of complete pairs of socks that you have left. (a) What is Cov (Xi , Xj ) where 1 i, j 10 and i = j? [4 points] (b) What is Cov (Xi , Xj ) where 1 i, j 10 and i 6= j? [4 points] (c) What is Var(Y )? Give your answer as a simplified fraction. [7 points] Hint: You will want to use your answers to the previous parts