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# ng be a random sample where each yn has mean and

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Unformatted text preview: i ji = 1, ..., ng be a random sample where each Yn has mean µ and variance σ2 . Then, the CTL states that p Yn n Melissa Tartari (Yale) µ a σ Econometrics N (0, 1) 14 / 27 Asymptotic Normality: the Central Limit Theorem I Let fYi ji = 1, ..., ng be a random sample where each Yn has mean µ and variance σ2 . Then, the CTL states that p Yn n µ a σ N (0, 1) That is, the average from any population, when standardized (recall 2 that Var Y n = σ ), has an asymptotic standard normal distribution. n Melissa Tartari (Yale) Econometrics 14 / 27 Asymptotic Normality: the Central Limit Theorem II p To use the de…nition of asymptotic normality let Zn each n so that you have a sequence fZn jn = 1, 2...g = M elissa Tartari (Yale) p Y1 1 Econometrics σ µ p Y2 ,2 µ σ n Yn µ σ for , ... 15 / 27 Asymptotic Normality: the Central Limit Theorem II p To use the de…nition of asymptotic normality let Zn each n so that you have a sequence fZn jn = 1, 2...g = p Y1 1 σ µ p Y2 ,2 µ σ n Yn µ σ for , ... Then, the CLT says that for any z th...
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## This note was uploaded on 02/13/2014 for the course ECON 350 taught by Professor Donaldbrown during the Fall '10 term at Yale.

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