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Tutorial 10, STAT1301 Fall 2010, 30NOV2010, MB103@HKU By Joseph Dong

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Sure Convergence Almost Sure Convergence Convergence in Probability Convergence in Distribution StrongestStrongerStrongWeak 6

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CLT WLLN SLLN 8

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One consequence of CLT is we can now at least approximate the distribution of an IID sum by normal distribution. Binomial Binomial is an IID sum of Bernoullis Poisson Poisson is an IID sum of Poissons Negative Binomial Negative Binomial is an IID sum of Geometrics Negative Binomial Negative Binomial is also an IID sum of Negative Binomials Gamma Gamma is an IID sum of Exponentials Gamma Gamma is also an IID sum of Gammas Chisq Chisq is an IID sum of Chisqs All of the above (and many others) can be approximated by appropriately parameterized Normal distributions. 9

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