Probability
M08 — Fall 24
Contents
Preface
1 Recap of measure theory
2 Foundations of probability theory
2.1 Probability spaces
2.2 Random variables
2.3 Expectation
2.4 The classical laws
2.5 Cumulative distribution function
2.6 The \(\sigma\)-algebra generated by a random variable
2.7 Moments and inequalities
3 Independence
3.1 Independent events
3.2 Intermezzo: monotone class lemma*
3.3 Independent \(\sigma\)-algebras and random variables
3.4 The Borel-Cantelli lemma
3.5 Sums of independent random variables
4 Convergence of random variables
4.1 Notions of convergence
4.2 The law of large numbers
4.3 Convergence in law
4.4 Characteristic function
4.5 The central limit theorem
Probability
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