There are two parts to the lecture notes for this class: The Brief Note, which is a summary of the topics discussed in class, and the Application Example, which gives real-wolrd examples of the topics covered.
| WEEK # | TOPICS | BRIEF NOTES | APPLICATION EXAMPLES |
|---|---|---|---|
| Part 1: Introduction to Probability | |||
| 1 | Events and their Probability, Elementary Operations with Events, Total Probability Theorem, Independence, Bayes' Theorem | 1 (PDF) |
1 (PDF) 2 (PDF) 3 (PDF) 4 (PDF) |
| 2-3 | Random Variables and Vectors, Discrete and Continuous Probability Distributions |
2 (PDF) 3 (PDF) 4 (PDF) |
5 (PDF) 6 (PDF) 7 (PDF) 8 (PDF) |
| 4 | Functions of Random Variables and Derived Distributions | 5 (PDF) |
9 (PDF) 10 (PDF) 11 (PDF) |
| 5-6 |
Expectation of Random Variables and Functions of Random Variables Moments of Variables and Vectors |
6 (PDF) |
12 (PDF) 13 (PDF) 14 (PDF) |
| 7 | Conditional Second Moment Analysis | 7 (PDF) |
15 (PDF) 16 (PDF) |
| 8 | Selected Distribution Models: Normal, Lognormal, Extreme, Multivariate Normal Distributions | 8 (PDF) | |
| Part 2: Introduction to System Reliability | |||
| 9 | Time-invariant Second-Moment Reliability Analysis and Time-Invariant Full-Distribution Reliability Analysis | 9 (PDF) | 17 (PDF) |
| Part 3: Introduction to Statistics | |||
| 10 | Point Estimation of Distribution Parameters: Methods of Moments and Maximum Likelihood, Bayesian Analysis | 10 (PDF) | 18 (PDF) |
| 11 | Simple and Multiple Linear Regression | 11 (PDF) | 19 (PDF) |