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# Properties - Econ 410 Fall 2006 TA Ignacio Monzon1 Useful Properties Properties of Expectations Assume X and Y are random variables and a and b are

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Useful Properties Econ 410 - Fall 2006. TA: Ignacio Monzon 1 Properties of Expectations Assume X and Y are random variables and a and b are given constants. Property 1 The expected value of a constant is the same constant: E ( a ) = a Property 2 The expected value is a linear operator: E ( aX + b ) = aE ( X ) + b Property 3 E ( aX + bY ) = aE ( X ) + bE ( Y ) Things that are NOT TRUE in general It is NOT true that E X Y ± = E ( X ) E ( Y ) it is NOT true that E ( X 2 ) = E ( X ) 2 Properties of Variances Property 1 V ar ( X ) = 0 if and only if X is a constant (and then, not a random variable) Property 2 V ar ( aX + b ) = a 2 V ar ( X ) Property 3 V ar ( aX + bY ) = a 2 V ar ( X ) + b 2 V ar ( Y ) + 2 abCov ( X;Y ) : Properties of Conditional Expectations Assume X and Y are random variables and that g ( ± ) and h ( ± ) are two functions. Property 1 E [ g ( X ) j X ] = g ( X ) Property 2 E [ g ( X ) Y + h ( X ) j X ] = g ( X ) E ( Y j X ) + h ( X ) Property 3 If X and Y are independent, then

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## This note was uploaded on 07/28/2010 for the course ECON 410 taught by Professor Staff during the Fall '08 term at Wisconsin.

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Properties - Econ 410 Fall 2006 TA Ignacio Monzon1 Useful Properties Properties of Expectations Assume X and Y are random variables and a and b are

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