Probability

Jim Pitman is a Professor in the Departments of Statistics and Mathematics in the University of California at Berkeley, USA.

• 1 Introduction.- 1.1 Equally Likely Outcomes.- 1.2 Interpretations.- 1.3 Distributions.- 1.4 Conditional Probability and Independence.- 1.5 Bayes’ Rule.- 1.6 Sequences of Events.- Summary.- Review Exercises.- 2 Repeated Trials and Sampling.- 2.1 The Binomial Distribution.- 2.2 Normal Approximation: Method.- 2.3 Normal Approximation: Derivation (Optional).- 2.4 Poisson Approximation.- 2.5 Random Sampling.- Summary.- Review Exercises.- 3 Random Variables.- 3.1 Introduction.- 3.2 Expectation.- 3.3 Standard Deviation and Normal Approximation.- 3.4 Discrete Distributions.- 3.5 The Poisson Distribution.- 3.6 Symmetry (Optional).- Summary.- Review Exercises.- 4 Continuous Distributions.- 4.1 Probability Densities.- 4.2 Exponential and Gamma Distributions.- 4.3 Hazard Rates (Optional).- 4.4 Change of Variable.- 4.5 Cumulative Distribution Functions.- 4.6 Order Statistics (Optional).- Summary.- Review Exercises.- 5 Continuous Joint Distributions.- 5.1 Uniform Distributions.- 5.2 Densities.- 5.3Independent Normal Variables.- 5.4 Operations (Optional).- Summary.- Review Exercises.- 6 Dependence.- 6.1 Conditional Distributions: Discrete Case.- 6.2 Conditional Expectation: Discrete Case.- 6.3 Conditioning: Density Case.- 6.4 Covariance and Correlation.- 6.5 Bivariate Normal.- Summary.- Review Exercises.- Distribution Summaries.- Discrete.- Continuous.- Beta.- Binomial.- Exponential.- Gamma.- Geometric and Negative Binomial.- Hypergeometrie.- Normal.- Poisson.- Uniform.- Examinations.- Solutions to Examinations.- Appendices.- 1 Counting.- 2 Sums.- 3 Calculus.- 4 Exponents and Logarithms.- 5 Normal Table.- Brief Solutions to Odd-Numbered Exercises.