ENEE 324Engineering ProbabilityInstructor: Dr. Steven A. TretterOffice: AVW 1337Telephone: University: (301) 405-3670 Home: (301) 622-3976e-mail: [email protected]: Amirali Sharifie-mail: [email protected] web site: www.ece.umd.edu/~tretterText: A. Leon-Garcia, Probability and Random Processes for Electrical Engineering, 2nd ed.,Addison-Wesley, 1994HOMEWORK• Homework will be assigned each week after the related material is presented in class.It may be assigned Monday and/or Wednesday.• Homework is due at the beginning of the next class after it was assigned.• Late homework will not be accepted but the two lowest scores will be dropped.• Homework solutions will be discussed in the recitation sections.EXAMSThere will be two exams during the semester and a comprehensive final exam. All examswill be closed book. No calculators, notebook computers, etc., will be allowed.Final Exam Date: Saturday, December 16, 8:00am – 10:00 amChapters Percent of GradeEXAM 1 1–3 25EXAM 2 4–6 25FINAL EXAM Comprehensive 40Homework 10COURSE OUTLINEI. Introduction (Chapter 1)A. Reasons for studying probabilityB. Brief historyII. Basic Concepts of Probability (Chapter 2)A. Elementary set theoryB. Random Experiments1. experiments and outcomes2. The sample space3. eventsC. The Probability Space1. Probability Measure2. Axioms of Probability3. Useful corollaries4. Discrete and continuous sample spacesD. Discrete Probability Spaces1. Permutaions and Combinations2. Probabilities for experiments with equally likely outcomesE. Conditional Probability1. Definition2. Total Probability Rule3. Probability Trees4. Bayes’ RuleF. Independent EventsG. Repeated ExperimentsIII. One-Dimensional Random Variables (Chapter 3)A. Definition of a random variableB. Discrete random variables1. Probability mass function2. Examples – uniform, binomial, PoissonC. Cumulative distribution function (cdf)D. Probability density function (pdf)E. Continuous random variables1. Examples – uniform, exponential, Gaussian, . . .F. One function of one random variable1. Finding new cdf and then pdf2. New pdf from old by Transformation Theorem2IV. Two and Higher Dimensional Random Variables (Chapter 4)A. Joint and marginal probability mass functionsB. Joint cdf and pdfC. conditional pdfD. Independent random variablesE. One function of two random variablesF. Two functions of two random variablesG. Extension to higher dimensional random variablesV. Expected Values (Chapters 3 and 4)A. The mean or expected value of a random variable (3.6)B. Expected value of a function of a random variable (3.6)C. Variance (3.6)D. Chebyshev’s Inequality (3.7)E. Covariance and correlation coefficient (4.7)F. Moment generating and characteristic functions (3.9, 4.7, 4.8)VI. Limit Theorems (Chapter 5)A. Law of Large NumbersB. Central Limit TheoremVII. Random or Stochastic Processes (Chapter 6)A. Ensemble of sample functionsB. n-th order statisticsC. Mean and autocorrelation functionsD. Random telegraph and binary random wavesVIII. Stationary Random Processes (Chapters 6 and 7)A. Definition of wide-sense stationarityB. Mean and autocorrelation functionsC. Power spectral densityD. Stationary processes and linear, time-invariant systemsE. Thermal noiseF. Shot noiseIX. Selected Additional