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Unformatted text preview: ) = 0.25 Var ( X | Y = 1 ) = 0.21 Var ( X | Y = 2 ) = 0.00 Def E ( X | Y = y ) = & x x P ( X = x | Y = y ) = & x x p X | Y ( x | y ) Denote by E ( X | Y ) that function of the random variable Y whose value at Y = y is E ( X | Y = y ). Note that E ( X | Y ) is itself a random variable, it depends on the ( random ) value of Y that occurs. E ( a 1 X 1 + a 2 X 2 | Y ) = a 1 E ( X 1 | Y ) + a 2 E ( X 2 | Y ) E ( E ( X | Y ) ) = E ( X ) E [ g ( Y ) X | Y ] = g ( Y ) E ( X | Y ) E [ g ( Y ) E ( X | Y ) ] = E [ g ( Y ) X ] E [ E ( X | Y ) | Y ] = E ( X | Y )...
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This note was uploaded on 10/22/2009 for the course STAT 410 taught by Professor Alexeistepanov during the Fall '08 term at University of Illinois at Urbana–Champaign.
- Fall '08