| Part 1: Introduction to Probability |
| 1 |
Events and their Probability, Elementary Operations with Events, Total Probability Theorem, Independence, Bayes' Theorem |
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| 2-3 |
Random Variables and Vectors, Discrete and Continuous Probability Distributions |
Mini-quiz 1 |
| 4 |
Functions of Random Variables and Derived Distributions |
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| 5-6 |
Expectation of Random Variables and Functions of Random Variables
Moments of Variables and Vectors |
Mini-quiz 2 |
| 7 |
Conditional Second Moment Analysis |
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| 8 |
Selected Distribution Models: Normal, Lognormal, Extreme, Multivariate Normal Distributions |
Mini-quiz 3 |
| Part 2: Introduction to System Reliability |
| 9 |
Time-invariant Second-moment Reliability Analysis and Time-invariant Full-distribution Reliability Analysis |
Mini-quiz 4 |
| Part 3: Introduction to Statistics |
| 10 |
Point Estimation of Distribution Parameters: Methods of Moments and Maximum Likelihood, Bayesian Analysis |
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| 11 |
Simple and Multiple Linear Regression |
Mini-quiz 5 |
| 12 |
Final Exam |
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