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Spring STA231C, 2006 Prof. W. Polonik HW # 1 1. (Simple linear rank statistics) Let Rn = (R1 , . . . , Rn ) be a random permutation, i.e. P (Rn = rn ) = 1 n! for all rn Sn (= set of all n! permutations of {1, . . . , n}). Let a1 , . . . , an and c1 , . . . , cn 1 1 2 be constants, and let cn n n and c n n (ci cn )2 . (Similarly dene an and i=1 i=1 2 ). a Show that (a) EaRi = an , (c) Let Tn 1 n 2 Var(aRi...
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Spring STA231C, 2006 Prof. W. Polonik
HW # 1
1. (Simple linear rank s...
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