A First Course in Probability
An elementary introduction to the theory of probability for students in mathematics, statistics, engineering, and the sciences. It covers the basic principles of combinatorial analysis, probability axioms, conditional probability, random variables, and limit theorems.
Course Overview
Content Summary
An elementary introduction to the theory of probability for students in mathematics, statistics, engineering, and the sciences. It covers the basic principles of combinatorial analysis, probability axioms, conditional probability, random variables, and limit theorems.
A classic, comprehensive foundation to the mathematical theory and applications of probability.
Author: Sheldon Ross
Acknowledgments: Hossein Hamedani, Joe Blitzstein, Peter Nuesch, Ivan Ardestani, and several university reviewers/contributors are credited for accuracy and feedback.
Learning Objectives
- Apply the Basic and Generalized Principles of Counting to multi-stage experiments.
- Differentiate between and calculate permutations and combinations for both distinct and indistinguishable objects.
- Prove combinatorial identities using algebraic induction and logical combinatorial arguments.
- Define sample spaces and events for diverse experiments and apply DeMorgan's laws to set operations.
- Calculate probabilities using the three fundamental Axioms of Probability and simple propositions (complements, unions, and subsets).
- Solve complex combinatorial problems involving equally likely outcomes, such as poker hands, the Matching problem, and the Birthday problem.
- Define and calculate conditional probabilities using the formula P(E|F) = \frac{P(EF)}{P(F)}.
- Apply Bayes's Formula to solve complex problems involving multiple hypotheses and diagnostic testing.
- Distinguish between independent and conditionally independent events in practical scenarios like genetics and engineering.
- Define discrete random variables and compute their PMFs and CDFs.