Lecture Notes

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)

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