EE104: Probabilistic Systems Analysis
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 101A, Halligan Hall
- Lectures: Tuesdays and Thursdays, 10:30AM – 11:45 AM, Halligan Hall, Room 111B
- Office Hours
- Official: Tuesdays and Thursdays, 2:00PM – 3:00 PM, Halligan Hall, Room 101A
- Email Prof. Miller for an appointment
- Stop by Prof. Miller’s Office
Officially: Math 42
- Knowledge of differentiation and integration of single and multi-variable (mostly two variables) functions
- There will be regular computational assignments, so it would be helpful to have had some experience with a tool such as Matlab or Mathematica. Low level languages such as C or Python are fine to use as well.
Use of Piazza
This term we will be using Piazza for class discussion. The system is highly catered to getting you help fast and efficiently. Rather than emailing questions to the teaching staff, I encourage you to post your questions on Piazza
Find our class page at: https://piazza.com/class/jlcohws8peklh
- There will be 10 or 11 problem sets.
- They will count for 10% of the grade.
- The lowest problem set grade will be dropped if a course evaluation receipt is emailed to Prof. Miller
- All problem sets should be handed into the EE 104 box located in Halligan 101 by 5PM on the due date
- No late assignments will be accepted
- There will be 4-5 assignments in addition to the problem sets designed to provide experience with "processing" data using probabilistic and statistical computational methods
- These will count for 10% of the grade
- Two in class exams will be given each worth 25%
- A last exam worth 30% of the grade will be given during finals week
Requests for re-grades
- Students have one week from the time an assignment or exam is returned to dispute a grade. All such requests must be made in writing and submitted to Prof. Miller along with the material to be reviewed.
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.
- Probability and Stochastic Processes, A Friendly Introduction for Electrical and Computer Engineers, by Roy Yates and David Goodman, 3rd Edition, Wiley, 2014.
- Probabilistic Methods of Signal and System Analysis, by George R. Cooper and the late Clare D. McGillem, Oxford, 1998
- Introduction to Probability, by Dimitri P. Bertsekas and John N. Tsitsiklis, Athena Scientific, 2002
- Probabilistic Systems and Random Signals by A. H. Haddad, Prentice Hall, Upper, 2006
- Probability and Random Processes for Electrical Engineering by Leon Garcia, Addison Wesley, 1994
- First Course in Probability, by Sheldon Ross, Prentice Hall, 2005
- Probability, Random Processes, and Statistical Analysis by Hisashi Kobayashi, Brian L. Mark, and William Turin, Cambridge University Press, 2011.
|Sept 4||Introduction and basic set theory|
|Sept 6||Axioms of probability and basic models|
|Sept 11||Conditional probability and Bayes Law|
|Sept 13||Bayer Law and Independence and|
|Sept 20||Discrete random variables (RVs), Probability mass functions (PMFs), Bernoulli process|
|Sept 25||Poisson RV, Cumulative distribution functions (CDFs), expectation, mean, and variance for discrete RVs|
|Sept 27||Probability density functions (PDFs), CDFs, and expectation for continuous RVs|
|Oct 2||Expectations for continuous RVs, common PDFs, Gaussian RVs|
|Oct 4||First In-Class Exam (tentative)|
|Oct 9||NO CLASS, MONDAY SCHEDULE|
|Oct 11||Jointly distributed discrete and continuous RVs, marginal distributions|
|Oct 16||Expected values for pairs of RVs, Covariance, Correlation, and Independence|
|Oct 18||Bivariate Gaussian models, Multivariate Probability Models|
|Oct 23||Bivariate Gaussian models, Multivariate Probability Models|
|Oct 25||Derived distributions for pairs of discrete random variables, derived distribution for continuous random variables|
|Oct 30||Derived distribution for pairs of continuous random variables|
|Nov 1||Conditioning a single random variable on an event and conditional expectations|
|Nov 6||Conditioning pairs of random variables on an event and conditioning on a random variable|
|Nov 8||Conditioning pairs of random variables on an event and conditioning on a random variable|
|Nov 13||Second in class exam (tentative)|
|Nov 15||Conditional expected value and bivariate Gaussians revisited. Sums of random variables|
|Nov 20||Central limit theorem and applications|
|Nov 22||No class: Thanksgiving Break|
|Nov 27||Properties of the sample mean, probability inequalities|
|Nov 29||Properties of point estimators, weak law of large numbers, Confidence intervals|
|Dec 4||Introduction to hypothesis testing and significance testing|
|Dec 6||Binary hypothesis testing|
The syllabus page shows a table-oriented view of the course schedule, and the basics of course grading. You can add any other comments, notes, or thoughts you have about the course structure, course policies or anything else.
To add some comments, click the "Edit" link at the top.