1.151 | Spring 2005 | Graduate

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.

Part 1: Introduction to Probability
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)


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
9 Time-invariant Second-Moment Reliability Analysis and Time-Invariant Full-Distribution Reliability Analysis 9 (PDF) 17 (PDF)
Part 3: Introduction to Statistics
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)

Course Info

As Taught In
Spring 2005
Learning Resource Types
Lecture Notes
Problem Sets