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Contents

• V Full version
• 0 Introduction
• 1 Classical probability
• 1.1 Classical probability
• 1.2 Counting
• 1.3 Stirling's formula
• 2 Axioms of probability
• 2.1 Axioms and definitions
• 2.2 Inequalities and formulae
• 2.3 Independence
• 2.4 Important discrete distributions
• 2.5 Conditional probability
• 3 Discrete random variables
• 3.1 Discrete random variables
• 3.2 Inequalities
• 3.3 Weak law of large numbers
• 3.4 Multiple random variables
• 3.5 Probability generating functions
• 4 Interesting problems
• 4.1 Branching processes
• 4.2 Random walk and gambler's ruin
• 5 Continuous random variables
• 5.1 Continuous random variables
• 5.2 Stochastic ordering and inspection paradox
• 5.3 Jointly distributed random variables
• 5.4 Geometric probability
• 5.5 The normal distribution
• 5.6 Transformation of random variables
• 5.7 Moment generating functions
• 6 More distributions
• 6.1 Cauchy distribution
• 6.2 Gamma distribution
• 6.3 Beta distribution*
• 6.4 More on the normal distribution
• 6.5 Multivariate normal
• 7 Central limit theorem
• 8 Summary of distributions
• 8.1 Discrete distributions
• 8.2 Continuous distributions