Sheet10 - Statistics 330/600 2005: Sheet 10 Due: Thursday 7...

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Statistics 330/600 Due: Thursday 7 April 2005: Sheet 10 *(10.1) Suppose X L 1 (Ä, F , P ) and Y = P ( X | F 0 ) for some sub-sigma-Feld F 0 of F . Suppose W is an F 0 -measurable random variable for which XW L 1 (Ä, F , P ) . (i) Show that YW L 1 (Ä, F , P ) and P ( XW ) = P ( YW ) . Hint: Consider X ± and W ± . Note that Y = P ( X + | F 0 ) P ( X | F 0 ) almost surely. (ii) Show that Y 0 almost surely if P ( XW ) 0 for every bounded, F 0 -measurable,
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This note was uploaded on 11/21/2009 for the course STAT 330 taught by Professor Davidpollard during the Spring '09 term at Yale.

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