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Problem 5. Roll a fair die 100 times (in each roll of the die, it produces a number equally likely in {1, 2, 3, 4, 5, 6}). For 1 S k S 6, let N1, be the number of times we roll on the number k. (a) Compute the conditional expectation IE(N2 + N4 | N4 + N6 = 30). (b) Compute the correlation between N1 + N2 and N2 + N3