ENEE324: Engineering Probability – Course Syllabus Spring 2009 Instructor: Joseph JaJa http://www.umiacs.umd.edu/~joseph/classes/enee324/index.htm Course Objectives: Axioms of probability; conditional probability and Bayes' rule; random variables, probability distribution and densities: functions of random variables: weak law of large numbers and central limit theorem. Introduction to random processes, hypothesis testing, and Markov chains. Prerequisite: ENEE 322 and completion of all lower-division technical courses in the ECE curriculum Textbook (required): Yates and Goodman, Probability and Stochastic Processes (second edition), Wiley. Core Topics: 1. Introduction to Probability (Chapter 1)  Sample Space and Events  Axioms of Probability  Computing Probabilities  Conditional Probability and Independence  Sequential Experiments  Independent Trials 2. Random Variables (Chapters 2 and 3)  Discrete Random Variables and Probability Mass Function  Continuous Random Variables and Probability Density Function  Functions of a Random Variable  Expected Value, Variance and Standard Deviation  Important Families of Discrete and Continuous Random Variables  Conditional Distributions and Conditional Expectations 3. Multiple Random Variables (Chapters 4 and 5*)  Joint Probability Functions  Marginal Probability Functions  Functions of Multiple Random Variables  Conditional Distributions and Conditional Expectations  Covariance and Correlation  Independent Random Variables 4. Sums of Random Variables (Chapter 6*)  Probability Density Function of Sums of Random Variables  Moment Generating Functions  Central Limit Theorem 5. Parameter Estimation (Chapter 7*)  Sample Mean and Expected Value  Estimates of Model Parameters  Weak Law of Large Numbers  Confidence Intervals6. Hypothesis Testing (Chapter 8*)  Basic Concepts  Binary Hypothesis Testing  Maximum A Posteriori and Maximum Likelihood Tests  Multiple Hypothesis Testing 7. Stochastic Processes (Chapter 10*)  Types of Stochastic Processes  Independent, Identically Distributed Random Sequences  Poisson Processes  Stationary Processes 8. Optional: Markov Chains (Chapter 12*)  Discrete Markov Chains  Limiting State Probabilities  Limit Theorems for Irreducible Finite Markov Chains Starred chapters are partially covered. Grading Policy: Midterm Exams: 15% each (February 26, April 2, April 30) Homework: 20% (assigned after each lecture, collected by the end of the next lecture, returned in recitations) Final Exam: 35% (Comprehensive, 10:30-12:30, May 20) Late Assignments: No late assignments will be accepted but the assignment with the lowest score will not be counted. Office Hours by Instructor (3433 A.V. Williams Bldg): Tu, Th 1:00 – 2:30 and by email appointment. Additional office hours will be offered by the TAs. Contact Information: [email protected]; 301-405-1925. The University of Maryland, College Park has a nationally recognized Code of Academic Integrity, administered by the Student Honor Council. This Code sets standards for academic integrity at Maryland for all undergraduate and graduate students. As a student you are responsible for upholding these standards for this course. It is very important for you to be aware of the consequences of cheating, fabrication, facilitation, and plagiarism. For more information on the Code of Academic Integrity or the Student Honor Council, please visit http://www.studenthonorcouncil.umd.edu/whatis.html