Uncertainty in Engineering

Instructor(s): Prof. Daniele Veneziano

MIT Course Number: 1.010

As Taught In: Fall 2008

Level: Undergraduate

Course Description

This course gives an introduction to probability and statistics, with emphasis on engineering applications. Course topics include events and their probability, the total probability and Bayes’ theorems, discrete and continuous random variables and vectors, uncertainty propagation and conditional analysis. Second-moment representation of uncertainty, random sampling, estimation of distribution parameters (method of moments, maximum likelihood, Bayesian estimation), and simple and multiple linear regression. Concepts illustrated with examples from various areas of engineering and everyday life.

Lecture Notes:

1 Events and their probability (PDF)
2 Random variables: discrete distributions (PDF)
3 Random variables: continuous distributions (PDF)
4 Random vectors (PDF)
5 Functions of random variables and vectors (PDF)
6 Second-moment characterization of random variables and vectors; second-moment (SM) and first-order second-moment (FOSM) propagation of uncertainty (PDF)
7 Conditional second-moment analysis (PDF)
8 Selected distribution models (PDF)
9 Point and interval estimation of distribution parameters (PDF)

Application Examples:

1 Reliability of systems with various element configurations (PDF) Probability of combinations of events; binomial and Poisson distributions
2 Evaluation of natural and man-made risks (PDF) Total probability theorem
3 Extra-terrestrial life and the design of experiments (PDF) Bayes’ theorem
4 Earthquake prediction from imperfect premonitory signs (PDF) Bayes’ theorem (cont.)
5 Is the series of rainy/non-rainy days a Bernoulli trial sequence? (PDF) Bernoulli trial sequence and dependence in binary time series
6 Are the sequences of bus and earthquake arrivals Poisson? (PDF) Exponential and Poisson distributions
7 Distribution mixtures (PDF) Distribution mixtures
8 Old better than new, new better than old… (PDF) Hazard function
9 Relation between storm duration and precipitation intensity (PDF) Joint, marginal and conditional distributions
10 Reliability of a building under extreme wind loads: choosing the design wind speed (PDF) Independent random variables
11 Distribution of the maximum of independent identically-distributed variables (PDF) Functions of several random variables
12 Distribution of waves and wave loads in a random sea (PDF) Functions of random variables and reliability analysis
13 Design load factors for structural columns (PDF) Propagation of uncertainty through linear formulas: second-moment analysis
14 Probabilistic analysis of foundation settlement (PDF) FOSM analysis for functions of many variables
15 Uncertainty updating using noisy observations (PDF) Conditional second-moment analysis
16 Prediction of daily temperatures using several past observations (PDF) Conditional second moment analysis with vectors
17 Sums of iid random variables (PDF) Sums of iid random variables
18 Designing the checkout system of a supermarket (PDF) Stochastic system; Monte Carlo simulation
19 Comparison of estimators for the upper limit of the uniform distribution (PDF) Parameter estimation


Homework 1 (PDF)
Homework 2 (PDF)
Homework 3 (PDF)
Homework 4 (PDF)
Homework 5 (PDF)
Homework 6 (PDF)
Homework 7 (PDF)
Homework 8 (PDF)
Homework 9 (PDF)
Homework 10 (PDF)


The five short quizzes and the final exam from the class are presented here.

Mini-quiz 1 (PDF)
Mini-quiz 2 (PDF)
Mini-quiz 3 (PDF)
Mini-quiz 4 (PDF)
Mini-quiz 5 (PDF)
Final exam (PDF)

Download Course Materials:

This package contains the same content as the online version of the course, except for any audio/video materials and other interactive file types.

Download here.

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