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ec41lecture9

# ec41lecture9 - Statistics for Economists Lecture 9 Kata...

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Statistics for Economists Lecture 9 Kata Bognar UCLA Properties of the Sample Mean Estimation Point Estimators Continuous Random Variables Statistics for Economists Lecture 9 Kata Bognar UCLA October 26, 2010

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Statistics for Economists Lecture 9 Kata Bognar UCLA Properties of the Sample Mean Estimation Point Estimators Continuous Random Variables Announcements Homework 3 is due on Thursday. Class feedback.
Statistics for Economists Lecture 9 Kata Bognar UCLA Properties of the Sample Mean Estimation Point Estimators Continuous Random Variables Last Lecture Sum of random variables Expected value of the sample mean

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Statistics for Economists Lecture 9 Kata Bognar UCLA Properties of the Sample Mean Estimation Point Estimators Continuous Random Variables Today’s Outline 1 Variance of the sample mean 2 Estimation 3 Continuous random variables 4 Readings: TH, Chapter, 2.4, 3.2 Suggested readings: WS, Chapter 6.1 5 Readings for next class: TH, Chapter 3.4
Statistics for Economists Lecture 9 Kata Bognar UCLA Properties of the Sample Mean Estimation Point Estimators Continuous Random Variables Mean of the Sample Mean X 1 , X 2 , . . . , X n is a random sample from a distribution. The sample mean is a random variable, ¯ X = 1 n i X i . The expected value of the sample mean is equal to the mean of the distribution. μ ¯ x = E [ ¯ X ] = E " 1 n X i X i # = 1 n E " X i X i # = 1 n X i E [ X i ] = 1 n X i μ x = 1 n n μ x = μ x . Interpretation : The distribution of the sample mean is centered around the mean of the distribution.

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Statistics for Economists Lecture 9 Kata Bognar UCLA Properties of the Sample Mean Estimation Point Estimators Continuous Random Variables Variance of the Sample Mean The variance of the sample mean is equal to the variance of the distribution divided by the sample size. σ
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ec41lecture9 - Statistics for Economists Lecture 9 Kata...

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