Unformatted text preview: (b) X n → X and X n → Y almost surely. Show that P ( X = Y ) = 1. (c) X n → X and X n → Y in r th mean for some r ≥ 1. Show that P ( X = Y ) = 1. 4. Give examples of two (nonconstant) random variables X and Y such that (a) H¨older’s inequality reduces to an equality for some p > 1 and q > 1 (b) Minkowski’s inequality reduces to an equality for some p ≥ 1. 1...
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 Spring '08
 AMJAD
 Probability theory, Xn, J. MORIARTY

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