Course Syllabus

EE 140: Stochastic Processes, Detection and Estimation

Spring 2020


The goal of this class is the development of basic analytical tools for the modeling and analysis of random phenomena and the application of these tools to a range of problems arising in engineering, manufacturing, and operations research. The first portion of this class will cover introductory probability theory including sample spaces and probability, discrete and continuous random variables, conditional probability, expectations and conditional expectations, and derived distributions. The balance of the class will be concerned with statistical analysis methods including hypothesis testing, confidence intervals and nonparametric methods.


Prof. Eric Miller
Office: Room 101, Halligan Hall



  • Probability and Statistics: EE-24/104 or equivalent
  • Linear Systems: EE-23 or equivalent
  • Linear Algebra/Vector Spaces: Math 70 or equivalent

Tentative Grading Scheme

  • Homeworks: 30%
  • In-class mid-term exam: 30%
  • Final or final project: 40%

Academic Integrity

Tufts holds its students strictly accountable for adherence to academic integrity. The consequences for violations can be severe. It is critical that you understand the requirements of ethical behavior and academic work as described in Tufts’ Academic Integrity handbook. If you ever have a question about the expectations concerning a particular assignment or project in this course, be sure to ask me for clarification. The Faculty of the School of Arts and Sciences and the School of Engineering are required to report suspected cases of academic integrity violations to the Dean of Student Affairs Office. If I suspect that you have cheated or plagiarized in this class, I must report the situation to the dean.



  • Shynk, John J.  Probability, Random Variables, and Random Processes: Theory and Signal Processing Applications. Wiley, 2013.
  • Yates, Roy D., and David J. Goodman.  Probability and Random Processes: A Friendly Introduction for Electrical and Computer Engineers. Third Edition. Wiley, 2014.
  • Levy, Bernard C., Principles of Signal Detection and Parameter Estimation, Springer, 2008.  Tufts students should be able to access this text online here.
  • Notes and additional chapters from the two texts on the Canvas Site under Files/ClassNotes 


  • Leon-Garcia, Alberto. Probability, Statistics and Random Processes for Electrical Engineering. Third Edition, Prentice Hall, 2008
  • Kobayashi, Hisashi, Brian L. Mark, and William Turin. Probability, Random Processes, and Statistical Analysis: Applications to Communications, Signal Processing, Queuing Theory and Mathematical Finance. Cambridge University Press, 2011.
  • Gubner, John A., Probability and Random Processes for Electrical and Computer Engineers, Cambridge University Press, 2006.
  • Stark, Henry, and John William Woods.  Probability, Statistics and Random Processes for Engineers. Prentice-Hall, 2011.

Tentative Schedule

Date Topic
Jan. 16 Overview, Introduction to Random Vectors, First and Second Moments
Jan. 21 First and Second Moments of Random Vectors, Gaussian Models
Jan. 23 Gaussian Models, Introduction to Estimation, Minimum Mean Square Optimal Estimation
Jan. 28 MMSE and Maximum a Posteriori Estimation
Jan. 30 Maximum a Posteriori Estimation, Maximum Likelihood Estimation
Feb. 4 Cramer-Rao Bound, Vector Estimation, Bayes Linear Least Squares Estimation
Feb. 6 Binary and M-Ary Hypothesis Testing
Feb. 11 Binary and M-Ary Hypothesis Testing
Feb. 13 Binary and M-Ary Hypothesis Testing
Feb 18. Binary and M-Ary Hypothesis Testing
Feb. 20

No class: Monday schedule

Feb. 25 Asymptotic Analysis of Likelihood Ratio Tests
Feb. 27 Composite Hypothesis Testing
Mar. 3 Introduction to Random Processes
Mar. 5 Stationarity, First and Second Moment Analysis of Random Processes
Mar. 11 Independent and Identically Distributed Processes
Mar. 12 Mid-term Exam
Mar. 17 No class: spring break
Mar. 19 No class: spring break
Mar. 24 Markov Processes, Discrete Time Markov Chains
Mar. 26 Bernoulli Processes, Poisson Processes
Mar. 31 Wiener Process
Apr. 2 Linear Shift Invariant Systems and Wide Sense Stationary Processes, Power Spectral Density
Apr. 7 Cross-spectral Density and Optimal Estimation
Apr. 9 Optimal Estimation, Non-Causal Wiener Filter, Causal Wiener Filter
Apr. 14 Discrete Wiener Filters
Apr. 16 Discrete Wiener Filters
Apr. 21 TBD
Apr. 23 TBD


Course Summary:

Date Details Due