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Probability Theory: STAT310/MATH230 September 3,2016

Probability theory : STAT310/MATH230 December 15, 2020 Amir DemboE-mail of Mathematics, Stanford University, Stanford, CA 1. Probability , measure and Probability spaces, measures and Random variables and their Integration and the (mathematical) Independence and product measures54 chapter 2. Asymptotics: the law of large Weak laws of large The Borel-Cantelli Strong law of large numbers85 chapter 3. Weak convergence,cltand Poisson The Central Limit Weak Characteristic Poisson approximation and the Poisson Random vectors and the multivariateclt141 chapter 4. Conditional expectations and Conditional expectation: existence and Properties of the conditional The conditional expectation as an orthogonal Regular conditional Probability distributions171 chapter 5.

Chapter 3 is devoted to the theory of weak convergence, the related concepts of distribution and characteristic functions and two important special cases: the Central Limit Theorem (in short clt) and the Poisson approximation.

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