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Probability

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Author(s): R. Weber, ed. Dexter Chua
Series: Cambridge Mathematical Tripos Part IA Lecture Notes
Publisher: University of Cambridge
Year: 2015

Language: English
City: Cambridge
Tags: maths; mathematics; math; advanced; college; university; higher; further; pure; applied; statistics; probability; stats; stat; theory

Introduction
Classical probability
Classical probability
Counting
Stirling's formula
Axioms of probability
Axioms and definitions
Inequalities and formulae
Independence
Important discrete distributions
Conditional probability
Discrete random variables
Discrete random variables
Inequalities
Weak law of large numbers
Multiple random variables
Probability generating functions
Interesting problems
Branching processes
Random walk and gambler's ruin
Continuous random variables
Continuous random variables
Stochastic ordering and inspection paradox
Jointly distributed random variables
Geometric probability
The normal distribution
Transformation of random variables
Moment generating functions
More distributions
Cauchy distribution
Gamma distribution
Beta distribution*
More on the normal distribution
Multivariate normal
Central limit theorem
Summary of distributions
Discrete distributions
Continuous distributions