Lecture notes. Written from the material of MIT 6.041SC, licensed CC BY-NC-SA 4.0. Notes, not a transcript — reorganised and rewritten, carrying the same licence.
MIT 6.041SC¶
26 chapters, written from the course's material.
Contents¶
- Sample Spaces and the Axioms of Probability
- Conditional Probability and Bayes' Rule
- Independence of Events
- Counting Methods and Binomial Probabilities
- Random Variables, PMFs, and Expectation
- Conditional Expectation and Joint PMFs
- Multiple Random Variables and Independence
- Continuous Random Variables and the Normal Distribution
- Joint and Conditional Continuous Densities
- Derived Distributions and Bayesian Inference
- Derived Distributions, Convolutions, and Covariance
- Iterated Expectations and Total Variance
- The Bernoulli Process
- The Poisson Process
- Poisson Processes: Merging, Splitting, and Random Incidence
- Discrete-Time Markov Chains
- Steady-State Behavior of Markov Chains
- Markov Chain Dynamics and Absorption
- Limit Theorems and Sample Means
- The Central Limit Theorem
- Introduction to Bayesian Inference
- Least Mean Squares Estimation
- Classical Statistics and Parameter Estimation
- Linear Regression and Hypothesis Testing
- Classical Hypothesis Testing
- Hypergeometric Probabilities
Sources¶
The book carries CC BY-NC-SA 4.0.
| Offering | Original | Commit | Licence |
|---|---|---|---|
| MIT 6.041SC | ocw.mit.edu/courses/6-041sc-probabilistic-systems-analysis-and-applied-probability-fall-2013/ | — | CC BY-NC-SA 4.0 |