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3. (8 pt, 2 each) (Ross) Let X be a random variable taking values in the finite interval 0, c]. You may assume that X is discrete, though this is not necessary for this problem (a) Show that EX c and EX2 cEX (b) Use the inequalities above to show that Var(X) <c2[u(1-u)] u=EXE[0, 1]. where (e) Use the result of part (b) to show that Var(cx) se/ (d) Use the result in (c) to bound the variance of a random variable X taking values in an interval [a,히 with-oo < a < b < oo.

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