Textbook readings are given as page numbers from this text:
Ang, Alfredo H-S., and Wilson H. Tang. Probability Concepts in Engineering: Emphasis on Applications to Civil and Environmental Engineering. 2nd ed. New York, NY: John Wiley & Sons, 2006. ISBN: 9780471720645.
The following table provides information about the lecture (L) and recitation (R) sessions, and also shows when each of the lecture notes and application examples are presented.
| SES # | LECTURE TOPICS | TEXTBOOK READINGS | NOTES | EXAMPLES | KEY DATES |
|---|---|---|---|---|---|
| Events, their probability, and two important theorems | |||||
| L1 | Introduction. Events and their properties | 27-43 | |||
| L2 | Probability of events. Conditional probability, total probability theorem | 44-63 | 1 | ||
| L3 | Independence, Bayes' theorem | 63-65 | 1 | 2, 3, and 4 | Homework 1 out |
| R1 | Total probability and Bayes' theorems | ||||
| Random variables | |||||
| L4 | Discrete random variables. Bernoulli and geometric distributions | 81-88 and 105-111 | 5 | ||
| L5 | Binomial and Poisson distributions | 112-118 | 2 | 6 |
Homework 1 due Homework 2 out |
| R2 | Discrete random variables | ||||
| L6 | Continuous random variables. Uniform and exponential distributions | 118-122 | |||
| L7 | Hazard function, distributions of mixed type and distribution mixtures | 3 | 7 and 8 |
Homework 2 due Homework 3 out | |
| R3 | Continuous random variables, and hazard function | Quiz 1 | |||
| Random vectors | |||||
| L8 | Discrete random vectors | ||||
| L9 | Continuous random vectors | 131-136 | 4 | 9 |
Homework 3 due Homework 4 out |
| R4 | Random vectors | ||||
| Uncertainty propagation | |||||
| L10 | Functions of random variables; linear functions | 151-156 | |||
| L11 | Functions of random variables and vectors; monotonic and min/max functions | 157-160 and 172-174 | 10, 11, and 12 |
Homework 4 due Homework 5 out | |
| R5 | Functions of random variables | Quiz 2 | |||
| L12 | Functions of random vectors: sums of variables, gamma distribution | 122-125 | 5 | ||
| Second moment analysis | |||||
| L13 | Expectation, second moment characterization of random variables, probabilistic moments | 88-93 | Homework 5 due | ||
| R6 | Functions of random variables and vectors | ||||
| L14 | Second moment (SM) and first order second moment (FOSM) propagation of uncertainty for variables | 180-186 | Homework 6 out | ||
| L15 | Second moment characterization of random vectors; covariance and correlation coefficient | 138-140 | |||
| R7 | Probabilistic moments, SM and FOSM propagation of uncertainty for variables | Quiz 3 | |||
| L16 | SM and FOSM propagation of uncertainty for random vectors | 186-189 | Homework 6 due | ||
| L17 | SM and FOSM propagation of uncertainty for random vectors | 6 | 13 and 14 | Homework 7 out | |
| R8 | Variance, covariance, correlation, SM and FOSM propagation of uncertainty for random vectors | ||||
| Conditional second moment analysis | |||||
| L18 | Conditional SM analysis for variables | ||||
| L19 | Conditional SM analysis for vectors | 7 | 15 and 16 |
Homework 7 due Homework 8 out | |
| R9 | Conditional SM analysis for variables | Quiz 4 | |||
| Important distribution models | |||||
| L20 | Normal and lognormal distributions | 96-105 |
Homework 8 due Homework 9 out | ||
| R10 | Conditional SM analysis. Important distribution models | ||||
| L21 | Beta, extreme, and multivariate normal distributions | 127-131, 137, and 175-179 | 8 | 17 and 18 | |
| Statistics | |||||
| L22 | Estimation of distribution parameters: general principles | Homework 9 due | |||
| R11 | Estimation of distribution parameters | Quiz 5 | |||
| L23 | Method of moments | 246-251 | Homework 10 out | ||
| L24 | Maximum likelihood and Bayesian estimation | 251-254 and 346-357 | 9 | 19 | Homework 10 due |
| L25 | Simple and multiple linear regression | 306-309, 313-318, and 321-325 | |||
| R12 | Maximum likelihood and Bayesian estimation | ||||
| L26 | Pre-final review | ||||