Probability and Statistics in Engineering
Lecture Notes
There are two parts to the lecture notes for this class: The Brief Note, which is a summary of the topics discussed in class, and the Application Example, which gives real-wolrd examples of the topics covered.
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WEEK # |
TOPICS |
BRIEF NOTES |
APPLICATION EXAMPLES |
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Part 1: Introduction to Probability |
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1 |
Events and their Probability, Elementary Operations with Events, Total Probability Theorem, Independence, Bayes' Theorem |
1 (PDF) |
1 (PDF) 2 (PDF) 3 (PDF) 4 (PDF) |
|
2-3 |
Random Variables and Vectors, Discrete and Continuous Probability Distributions |
2 (PDF) 3 (PDF) 4 (PDF) |
5 (PDF) 6 (PDF) 7 (PDF) 8 (PDF) |
|
4 |
Functions of Random Variables and Derived Distributions |
5 (PDF) |
9 (PDF) 10 (PDF) 11 (PDF) |
|
5-6 |
Expectation of Random Variables and Functions of Random Variables Moments of Variables and Vectors |
6 (PDF) |
12 (PDF) 13 (PDF) 14 (PDF) |
|
7 |
Conditional Second Moment Analysis |
7 (PDF) |
15 (PDF) 16 (PDF) |
|
8 |
Selected Distribution Models: Normal, Lognormal, Extreme, Multivariate Normal Distributions |
8 (PDF) |
|
|
Part 2: Introduction to System Reliability |
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|
9 |
Time-invariant Second-Moment Reliability Analysis and Time-Invariant Full-Distribution Reliability Analysis |
9 (PDF) |
17 (PDF) |
|
Part 3: Introduction to Statistics |
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|
10 |
Point Estimation of Distribution Parameters: Methods of Moments and Maximum Likelihood, Bayesian Analysis |
10 (PDF) |
18 (PDF) |
|
11 |
Simple and Multiple Linear Regression |
11 (PDF) |
19 (PDF) |
Assignments
The assignments from the class are presented here, by week.
|
WEEK # |
TOPICS |
ASSIGNMENTS |
|
Part 1: Introduction to Probability |
||
|
1 |
Events and their Probability, Elementary Operations with Events, Total Probability Theorem, Independence, Bayes' Theorem |
Homework 1 (PDF) |
|
2-3 |
Random Variables and Vectors, Discrete and Continuous Probability Distributions |
Homework 2 (PDF) Homework 3 (PDF) |
|
4 |
Functions of Random Variables and Derived Distributions |
Homework 4 (PDF) |
|
5-6 |
Expectation of Random Variables and Functions of Random Variables Moments of Variables and Vectors |
|
|
7 |
Conditional Second Moment Analysis |
Homework 7 (PDF) |
|
8 |
Selected Distribution Models: Normal, Lognormal, Extreme, Multivariate Normal Distributions |
Homework 8 (PDF) |
|
Part 2: Introduction to System Reliability |
||
|
9 |
Time-invariant Second-Moment Reliability Analysis and Time-Invariant Full-Distribution Reliability Analysis |
Homework 9 (PDF) |
|
Part 3: Introduction to Statistics |
||
|
10 |
Point Estimation of Distribution Parameters: Methods of Moments and Maximum Likelihood, Bayesian Analysis |
Homework 10 (PDF) |
|
11 |
Simple and Multiple Linear Regression |
|
Exams
The two quizzes from the class are presented here, with the solutions to Quiz 1.
Quiz 2 (PDF)