Calendar

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        

Course Info

Learning Resource Types

assignment Problem Sets
grading Exams
notes Lecture Notes