1. Experiments, Models, and Probabilities 1) Applying Set Theory to Probability 2) Conditional Probability 3) Independence 2. Basics of Random Variables 1) Definitions 2) Probability Mass Function (PMF) 3) Families of Discrete Random Variables 4) Cumulative Distribution Function (CDF) 5) Probability Density Function (PDF) 6) Families of Continuous Random Variables 3. Random Variables and Expected Value 1) Conditional Probability Mass/Density Function 2) Probability Models of Derived Random Variables 3) Variance and Standard Deviation 4) Expected Value of a Derived Random Variable 4. Multiple Random Variables 1) Joint Cumulative Distribution Function 2) Joint Probability Mass/Density Function 3) Marginal PMF/PDF 4) Functions of Two Random Variables 5) Conditioning by a Random Variable 6) Independent Random Variables 5. Sums of Random Variables 1) Expected Values of Sums 2) PDF of the Sum of Two Random Variables 3) Moment Generating Functions 4) MGF of the Sum of Independent Random Variables 5) Random Sums of Independent Random Variables 6) Central Limit Theorem 6. Probability inequalities 7. Law of large numbers 8. Confidence Interval 9. Binary Hypothesis Testing

Probability and Stochastic Processes - A Friendly Introduction for Electrical and Computer Engineers," Second Edition