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# n Suppose X1,..., X are n iid random variables from the cumulative distribution func- tion F(x). Let Y = X; for i = 1,...,

n Suppose X1,..., X are n iid random variables from the cumulative distribution func- tion F(x). Let Y = X; for i = 1,..., n. We further know that X; and Y; have the same distribution. For 0.5 < p < 1, define Sp = inf{x : F(x) p}. Our interest is to estimate (p. Throughout this question, we assume that the probability density function f(x) of F(x) is continuous and positive for all x. Let and n n F(x) = 1

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