140A Key Topics

140A Key Topics - Key Topics Introduction to Econometrics...

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Unformatted text preview: Key Topics Introduction to Econometrics Mathematical Concepts Understand and verify the following properties & P J j =1 x j p j = x 1 p 1 + x 2 p 2 + ¡¡¡ + x J p J & P J j =1 ( x j + z j ) p j = P J j =1 x j p j + P J j =1 z j p j & & P J j =1 x j p j ¡ 2 = P J j =1 P J k =1 x j x k p j p k = P J j =1 x 2 j p 2 j + P J j =1 P J k =1 j 6 = k x j x k p j p k You should know this from prior coursework, but it is covered in the Random Variables lecture Probability Concepts Understand that for discrete random variables X , which takes J distinct values, and U , which takes K distinct values, & E ( X ) = P J j =1 x j ¡ P ( X = x j ) := & X & V ar ( X ) := E ( X ¢ & X ) 2 = P J j =1 ( x j ¢ & X ) 2 ¡ P ( X = x j ) & Cov ( X;U ) := E [( X ¢ & X ) ( U ¢ & U )] = P J j =1 P K k =1 ( x j ¢ & X ) ( u k ¢ & U ) ¡ P ( X = x j ;U = u k ) & E ( U j X = x j ) = P K k =1 u k ¡ P ( U = u k j X = x j ) & V ar ( U j X = x j ) := P K k =1 [ u k ¢ E ( U j X = x j )] 2 ¡ P ( U = u k j X = x j ) You should know this from prior coursework, but it is covered in the Random Variables lecture Understand and verify the following implications & E ( U j X ) = 0 means E ( U j X = x j ) = 0 for all ( x 1 ;:::;x J ) &...
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This note was uploaded on 09/04/2011 for the course ECON 140a taught by Professor Staff during the Fall '08 term at UCSB.

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140A Key Topics - Key Topics Introduction to Econometrics...

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