This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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 ) &...
View
Full
Document
This note was uploaded on 09/04/2011 for the course ECON 140a taught by Professor Staff during the Fall '08 term at UCSB.
 Fall '08
 Staff
 Econometrics

Click to edit the document details