 When you click the Amazon logo to the left of any citation and purchase the book (or other media) from Amazon.com, MIT OpenCourseWare will receive up to 10% of this purchase and any other purchases you make during that visit. This will not increase the cost of your purchase. Links provided are to the US Amazon site, but you can also support OCW through Amazon sites in other regions. Learn more. |
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.
Course calendar.
| 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 |
|
|
|
|