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.
Lecture Notes Files
| 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) |
| 12 |
Final Exam |
|
|