1.010 | Fall 2008 | Undergraduate

Uncertainty in Engineering


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.

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  
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

As Taught In
Fall 2008
Learning Resource Types
Problem Sets
Lecture Notes