Lecture 12 and 13.pdf - ECON41 MingGu 8/30...

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ECON 41  Statistics for Economists Ming Gu 8/30
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Grader Office Hour for Midterm Thursday, 8/31, 11am‐1pm, Alper Room, Bunche Hall You may take notes/photo, the original exam and scantron will not be  given back.
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Lecture 12: Law of Large Numbers and Central Limit  Theorem
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Chebyshev’s Inequality Suppose random variable X has mean  and variance . If k > 0, then 
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Theorem: The sample mean  ܺ of a random sample of size n from the  distribution with mean  and variance is such that
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Weak Law of Large Numbers Suppose that  ܺ , ܺ , … , ܺ are observations of a random sample from  the same distribution with the common mean  and variance Then, for any   > 0, we have
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Central Limit Theorem Let  ܺ denote the sample mean of a random sample of size n from the  distribution with mean  and variance . The distribution of is  approximately N(0,1) if n is large enough
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The ratio can be alternatively written as 
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