Part 1: Introduction to Probability
1 Events and their Probability, Elementary Operations with Events, Total Probability Theorem, Independence, Bayes’ Theorem

2-3 Random Variables and Vectors, Discrete and Continuous Probability Distributions

4 Functions of Random Variables and Derived Distributions

5-6 Expectation of Random Variables and Functions of Random Variables

Moments of Variables and Vectors

7 Conditional Second Moment Analysis

8 Selected Distribution Models: Normal, Lognormal, Extreme, Multivariate Normal Distributions Quiz on part 1 (1.5 hours, in class, open books and notes)
Part 2: Introduction to System Reliability
9 Time-invariant Second-Moment Reliability Analysis and Time-Invariant Full-Distribution Reliability Analysis

Part 3: Introduction to Statistics
10 Point Estimation of Distribution Parameters: Methods of Moments and Maximum Likelihood, Bayesian Analysis

11 Simple and Multiple Linear Regression Quiz on parts 2 and 3 (1.5 hours, in class, open books and notes)

Course Info

Learning Resource Types

grading Exams
notes Lecture Notes
assignment Problem Sets