ec41lecture8 (1)

ec41lecture8 (1) - Statistics for Economists Lecture 8 Kata...

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Unformatted text preview: Statistics for Economists Lecture 8 Kata Bognar UCLA Functions of Random Variables Estimation Point Estimation Statistics for Economists Lecture 8 Kata Bognar UCLA October 21, 2010 Statistics for Economists Lecture 8 Kata Bognar UCLA Functions of Random Variables Estimation Point Estimation Announcements • Homework 3 will be posted this afternoon, due on Oct 28. • Midterms can be viewed during TAs office hours. Statistics for Economists Lecture 8 Kata Bognar UCLA Functions of Random Variables Estimation Point Estimation Last Lecture • Expectations • Chebyshev inequality • Sums of random variables Statistics for Economists Lecture 8 Kata Bognar UCLA Functions of Random Variables Estimation Point Estimation Today’s Outline 1 Sums of random variables 2 Mean and variance of the sample mean 3 Estimation 4 Readings: TH, Chapter 2.5, 2.4 • Suggested readings: WS, Chapter 6.4, 7.1 - 7.2 5 Readings for next class: TH, 3.2 Statistics for Economists Lecture 8 Kata Bognar UCLA Functions of Random Variables Estimation Point Estimation Sum of Two Random Variables - Example X 2 Y = X 1 + X 2 X 1 1 2 1/6 1/12 1/12 1 1/3 1/6 1/6 = ⇒ y g ( y ) 1/6 1 5/12 2 3/12 3 1/6 Statistics for Economists Lecture 8 Kata Bognar UCLA Functions of Random Variables Estimation Point Estimation Independence of Random Variables- Example 1 X 1 and X 2 are not independent . • The joint p.m.f. of X 1 and X 2 X 2 X 1 1 1/2 1 1/2 • Marginal and conditional p.m.f. of X 1 X 1 f 1 ( x ) f 1 ( x | X 2 = 0) f 1 ( x | X 2 = 1) 1/2 (1/2)/(1/2) = 1 (0)/(1/2) = 0 1 1/2 (0)/(1/2) = 0 (1/2)/(1/2) = 1 Statistics for Economists Lecture 8 Kata Bognar UCLA Functions of Random Variables Estimation Point Estimation Independence of Random Variables- Example 2 X 1 and X 2 are independent ....
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ec41lecture8 (1) - Statistics for Economists Lecture 8 Kata...

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