Let X1, . . . , Xn be a sample (i.i.d.) from a
Chapter , Problem 5(choose chapter or problem)
Let \(X_{1}, \ldots, X_{n}\) be a sample (i.i.d.) from a distribution function, F, and let \(F_n\) denote the ecdf. Show that
\(\operatorname{Cov}\left[F_{n}(u), F_{n}(v)\right]=\frac{1}{n}[F(m)-F(u) F(v)]\)
where m = min(u, v). Conclude that \(F_{n}(u) \text { and } F_{n}(v)\) are positively correlated: If \(F_{n}(u)\) overshoots F(u), then \(F_{n}(v)\) will tend to overshoot F(v).
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