ECONOMETRIC THRY&PR ECON 482
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This 6 page Class Notes was uploaded by Miss Adeline Weimann on Wednesday September 9, 2015. The Class Notes belongs to ECON 482 at University of Washington taught by Richard Startz in Fall. Since its upload, it has received 25 views. For similar materials see /class/192465/econ-482-university-of-washington in Economcs at University of Washington.
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Date Created: 09/09/15
Economics 482 Professor Startz Mathematics Useful for Economics 482 Herein one can find some facts from mathematics likely to be useful for Econ 482 1 Sigma notation a 2x E x1 x2 ocm1 xquot Frequently we just write 2x and let 391 limits and subscripts be implicit 2 2 x x u x x u 2 2 i1 1 I I xl x1u1 x2x2uz b39 2 2 x2 xz x2 2x 1 2 11 11 Or 2 gt i 2 x xu 3 x xu i1 i1 I i1 I I L xlul x2 2 2 2 39 x2x2 x2 X 1 2 i1 H 2 From calculus K 31X zXz 1 jaX zX fy Zy 0t2 b 2 Sf 2Zy a 0 c argminZani 02 amp a n il page 2 3 From algebra 2 2 2 alx1 azx2 anxn a1 x1 alalex2 ala3xlx3 alanxlxn 2 2 a2a1x2x1 02x2 aza3x2x3 39 39 39 azanxzxn 2 2 ana1xnx1 anazxnxz 39 39 39 an xquot page 3 4 From statistics about population distributions If the probability density function pdt for a random variable x is f x then a Expected value i Ex 2 xi f xi for discrete distributions imin x ii Ex J x f xdx for continuous distributions b Variance i var x quotif xi Ex2 f xi for discrete distributions ii varx J x Ex2 f xdx for continuous distributions c Standard deviation i stddevx E varx If thejoint pdf for x and y is fxy then d Covariance 39 covxy if if xi Exyj Eyfxlyj for jmin y imjnx discrete distributions H covxy T Tx Exy Eyfxydxdy for foo foo continuous distributions H H page 4 e Correlation COVxy i corrxy E W page 5 5 From statistics about samples If the sample size is n then a Expected value mean l quot 1 x x b Variance c Covariance i covxy z zxxi y 3 H 6 From mathematical statistics If 6117 are constants and XY and Z are random variables a EaXaEX b EaX aEX c EaX bY aEX bEY Y a bX 39 YEYlbXEXl e varaX VarX f varaX a2 varX g varXEXEX2EX2EX2 page 6 I2quot corraXbY E i varX EXzi EX 0 c0VaXbY COVXY COVaXbY abc0VXY 39 COVX YZ COVXZ COVYZ covXXvarX X1EXEXYEYEXYEXEY i 00VXY EXYz39 EX 0 or EY 0 varaX bYa2varXb2varY2abcovXY abc0VXY c0rrXY azvarXbzvarY XNuoz 2 NO1 X NuX039 Y NuY039039XY E COVXY gt aX bY NauX bypazoj bza 2ab039XY