6. Consider n independent tosses of a coin with probability of a head equal to p. Let X be the numbers of heads and Y be the numbers of tails. (a) Show that E(X) + E(Y) = n. (b) Show that Cov(X, Y) = -Var(X). (c) Compute Corr(X, Y).
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Show that E(X) + E(Y) = n: - The expected value of X is E(X) = np, since the probability of getting a head in each toss is p and there are n tosses. - The expected value of Y is E(Y) = n(1-p), since the probability of getting a tail in each toss is 1-p and there Show more…
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