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Lecture_2 - Intro Review of Distribution Theory Inference...

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Intro Review of Distribution Theory Inference Intro to Least Square Relevant Reading Quantitative Economics and Econometrics Sorawoot Srisuma Lecture 2
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Intro Review of Distribution Theory Inference Intro to Least Square Relevant Reading Plan of Today°s Lecture 1. Quick review of distribution theory 2. Inference 3. Introduction to estimation by least square
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Intro Review of Distribution Theory Inference Intro to Least Square Relevant Reading Normal Distribution Let X ° N ° μ X , σ 2 X ±
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Intro Review of Distribution Theory Inference Intro to Least Square Relevant Reading Normal Distribution Let X ° N ° μ X , σ 2 X ± ± aX + c ° N ° a μ X + c , a 2 σ 2 X ±
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Intro Review of Distribution Theory Inference Intro to Least Square Relevant Reading Normal Distribution Let X ° N ° μ X , σ 2 X ± ± aX + c ° N ° a μ X + c , a 2 σ 2 X ± ± Let there be another RV Y ° N ° μ Y , σ 2 Y ±
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Intro Review of Distribution Theory Inference Intro to Least Square Relevant Reading Normal Distribution Let X ° N ° μ X , σ 2 X ± ± aX + c ° N ° a μ X + c , a 2 σ 2 X ± ± Let there be another RV Y ° N ° μ Y , σ 2 Y ± ± If Cov ( X , Y ) = 0 then X and Y are independent (generally only ± ( ² is true)
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Intro Review of Distribution Theory Inference Intro to Least Square Relevant Reading Related Distribution We will be concerned with χ 2 , t and F distributions Let Z = X ² μ X σ X ° N ( 0 , 1 ) :
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Intro Review of Distribution Theory Inference Intro to Least Square Relevant Reading Related Distribution We will be concerned with χ 2 , t and F distributions Let Z = X ² μ X σ X ° N ( 0 , 1 ) : ± Z 2 ° χ 2 1 and if you have many i (.i.d.) f Z i g p i = 1 then Z 2 1 + . . . + Z 2 p ° χ 2 p
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Intro Review of Distribution Theory Inference Intro to Least Square Relevant Reading Related Distribution We will be concerned with χ 2 , t and F distributions Let Z = X ² μ X σ X ° N ( 0 , 1 ) : ± Z 2 ° χ 2 1 and if you have many i (.i.d.) f Z i g p i = 1 then Z 2 1 + . . . + Z 2 p ° χ 2 p ± Let W ° χ 2 m then Z / q W m has a t m when Z and W are independent
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Intro Review of Distribution Theory Inference Intro to Least Square Relevant Reading Related Distribution We will be concerned with χ 2 , t and F distributions Let Z = X ² μ X σ X ° N ( 0 , 1 ) : ± Z 2 ° χ 2 1 and if you have many i (.i.d.) f Z i g p i = 1 then Z 2 1 + . . . + Z 2 p ° χ 2 p ± Let W ° χ 2 m then Z / q W m has a t m when Z and W are independent ± Let V ° χ 2 n then W m / V n has an F m , n when W and V are independent
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Intro Review of Distribution Theory Inference Intro to Least Square Relevant Reading From Last Week ± We have a random sample f X i g N i = 1 (with some unknown distribution) ± We are interested in learning about μ X = E ( X 1 ) ± Our estimator is μ X = X = 1 N N i = 1 X i Recall that: ± X is an unbiased estimator for μ X ± Var ° X ± = σ 2 X = σ 2 X / N
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Intro Review of Distribution Theory Inference Intro to Least Square Relevant Reading Hypothesis Testing (Normal) Suppose the random sample is distributed as N ° μ X , σ 2 X ± We consider the hypothesis that H 0 : μ X = μ X , 0 as opposed to H 1 : μ X 6 =
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