Ve401 Probabilistic Methods in Engineering

Volume: 30 lectures @ 90 minutes

Syllabus: Download Course Description (PDF)

Prerequisites: Vv286 or Vv256

Background and Goals: This course on basic elements of statistical and probabilistic methods focuses particularly on applications to engineering such as quality control, acceptance sampling and comparison of qualitative data. The goal is to introduce the student to statistical methods and give enough practice and familiarity so that these methods may be immediately applied in other courses, lab experiments and project work.

Key Words: Combinatorics and counting, basic concepts in probability, discrete and continuous probability distributions, joint distributions, descriptive statistics, estimation, hypothesis testing, non-parametric methods, analysis of categorical data, simple and multiple regression analysis, model selection, introduction to analysis of variance and experimental design.

Detailed Content:

The first part of the course introduces some basic elements of probability theory and combinatorics, with proofs of theorems demonstrated as far as practical within the time constraints of the course. Students are expected to have a good knowledge of the standard calculus material of the first three terms, including, but not limited to, polar coordinates in higher dimensions, integration of single- and multiple-variable functions, the theory of convergence of series and sequences of functions, the theory of matrices and linear maps as well as systems of ordinary differential equations.

The second part of the course discusses some basic statistical methods for testing statistical hypotheses and analyzing means, variances and proportions. The results of the first part are applied to practical problems. Students are required to comprehend and interpret formulations of real-life situations, use their judgement and apply the correct procedure to find a suitable solution to a given problem. In this respect, the required skill sets are closer to a physics or engineering course than a mathematics course.

The third part of the course touches upon categorical data analysis, simple and multiple linear regression and analysis of variance (ANOVA). For regression problems in particular, familiarity with matrix calculus is required.

The course makes use of the Mathematica software, for which all JI students have a free license. The commands necessary for implementing statistical methods are given in the lecture at regular intervals.

Term projects will be completed by groups of 4-5 students. See below for the term projects in Summer 2017.

Textbooks:

[MA] J. S. Milton and J. C. Arnold, Introduction to Probability and Statistics: Principles and Applications for Engineering and the Computing Sciences, 4th Edition, McGraw-Hill

[HMGB] Hines, Montgomery, Goldsman and Borror, Probability and Statistics in Engineering, 4th Edition, 2003, J. Wiley & Sons.

Overview:

Lecture	Subject	Textbook Chapter
1	Introduction to Probability and Counting	[MA] 1
2	Some Probability Laws	[MA] 2
3	Discrete Random Variables	[MA] 3
4	Discrete Random Variables	[MA] 3
5	Continuous Random Variables	[MA] 4
6	The Normal Distribution	[MA] 4
7	Reliability	[MA] 4
8	Bivariate Random Variables	[MA] 5
9	First Midterm Exam	[MA] 1-5
10	Descriptive Statistics	[MA] 6
11	Point Estimation and Estimators	[MA] 7
12	The Chi-Squared Distribution	[MA] 7
13	Independence of Sample Mean and Sample Variance	---
14	Interval Estimation of Mean and Variance	[MA] 7
15	Hypothesis Testing	[MA] 8
16	OC Curves and Acceptance Sampling	[HMGB] 11-1, 11-2; [MA] 16.5
17	Significance Testing	[MA] 8
18	Comparison of Two Proportions	[MA] 9
19	Comparison of Two Variances	[MA] 10
20	Comparison of Two Means	[MA] 10
21	Second Midterm Exam	[MA] 6-10
22	Categorical Data	[MA] 15
23	Simple Linear Regression	[MA] 11
24	Simple Linear Regression	[MA] 11
25	Multiple Linear Regression	[MA] 12
26	Multiple Linear Regression	[MA] 12
27	Analysis of Variance	[MA] 13
28	Analysis of Variance	[MA] 13
29	Pitfalls and Controversies in Statistics	---
30	Final Exam	[MA] 11-13, 15

Lecture Slides (2017 version; PDF)

Term Project 1 (2017 version; PDF)

Term Project 2 (2017 version; PDF)

Assignments (2017 version; PDF files):

(There will always be minor modifications from one iteration of the course to the next; if you are presently taking the course, your assignments may differ from these.)