econ 140 3 - Economics 140 Professor Enrico Moretti...

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Economics 140 Professor Enrico Moretti 02/08/10 Lecture 4 ASUC Lecture Notes Online is the only authorized note-taking service at UC Berkeley. Do not share, copy or illegally distribute (electronically or otherwise) these notes. Our student-run program depends on your individual subscription for its continued existence. These notes are copyrighted by the University of California and are for your personal use only. D O N O T C O P Y Sharing or copying these notes is illegal and could end note taking for this course. ANNOUNCEMENTS: Problem set 2 is due today. Please turn your problem set in to your GSI. There is no class next Monday because of the holiday, but discussion will still be held. I will send an email on whether a problem set will be assigned or not. LECTURE Recall that the definition of expected value is: For one variable E(x) = x ּ pr(x) For two variables E(x) = over x over y x ּ f(xy) = over x x over y f(xy) = over x f(x) Some properties of expected value are: If x 1 , x 2 , x 3 ,…x n are random variables then the E(x 1 +x 2 +x 3 …+x n ) = E(x 1 ) +E(x 2 ) + E(x 3 )…+E(x n ). If a is a number then E(a 1 x 1 + a 2 x 2 +a 3 x 3 …+a n x n ) = a 1 E(x 1 )+ a 2 E(x 2 )+ a 3 E(x 3 )+… a n E(x n ). Measures of association , such as covariance, describes how much two random variables move together. For ex: 1)Y X X and Y have positive covariance because if you increase X, you’re likely (on average) to increase Y. There is positive association between the two variables. 2)
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econ 140 3 - Economics 140 Professor Enrico Moretti...

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