Suppose the random variable e has cdf F(t). Let (u) =12[u (1/2)],0 < u < 1,

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Suppose the random variable e has cdf F(t). Let ϕ(u) =√12[u − (1/2)],0 < u < 1, denote the Wilcoxon score function.
(a) Show that the random variable ϕ[F(ei)] has mean 0 and variance 1.
(b) Investigate the mean and variance of ϕ[F(ei)] for any score function ϕ(u) which satisfies ∫10 ϕ(u) du = 0 and ∫10 ϕ2(u) du = 1.

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Introduction To Mathematical Statistics

ISBN: 9780321794710

7th Edition

Authors: Robert V., Joseph W. McKean, Allen T. Craig

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