Suppose I flip n independent biased coins such that the jth coin has probability j/n of being heads, for j = 1,..., n. Let Hn be a random variable equal to the total number of heads. %3D (a) What is the expectation of Hn? (b) What is the variance of Hn? (c) Use Markov's inequality to derive an upper bound on P(Hn > 9n/10).

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