Let X₁, X2,..., Xn be an IID sample from continuous distribution F. We are interested in estimating p = Pr(a ≤ x ≤ b). (a) Let be the nonparametric, plug-in estimator for p. Derive the formula for p. (b) Find the standard error of p. (c) Find an approximate 100(1-a)% confidence interval p.

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