RANDOM PROCESS (Date of document: 3rd Dec 2007) Course Code Course Status Level Semester Taught Credit Pre-requisites

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EEEB383 / EEEB384 Core Degree 4 3 Signal & System (EEEB233)

Assessments

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Quizzes

10%

Assignments

10%

Test 1

15%

Test 2

15%

Exam

50%

Lecturers

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Farah Hani Nordin, Noor Miza Bte. Muhamad Razali Office:

BN-0-23

Email:

[email protected]

EXT:

6091

Website (Download lecture notes): http://www.noormiza.net.tc/

Course Description : The course begins by reviewing fundamental theories and laws of probability which includes Bayes theorem, the law of total probability, conditional probability, permutation, combination and the concept of tree diagram. These basic concepts of probability will be used in discrete and continuous random variables where the concept of probability mass function, probability density function, cumulative density functions and the use of mixed random variables are explored. For two random variables, the joints for probability mass function, probability density function and cumulative density function are also introduced. The random variable concepts are then used in stochastic processes where the needs to study random variables in stochastic/random processes will be explained apart from the properties such as being independent and identically distributed or stationary stochastic process. The course will also cover the processing of random signal which covers the linear

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filtering of a random process, power spectral density, cross spectral density and the frequency domain filter relationships. Course Objectives

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1) To revise and extend on basic knowledge of probability. 2) To understand the characteristics and underlying theories of random variables. 3) To understand the characteristics and underlying theories of stochastic process. 4) To understand the underlying theories of random signal processing. Course Outline

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EXPERIMENTS MODELS AND PROBABILITY • Set Theory • Applying set theory to probability • Probability axioms • Some consequences of the axioms • Conditional probability • Independence • Sequential experiments and tree diagrams • Counting methods • Independent trials

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DISCRETE RANDOM VARIABLES • Definitions • Probability Mass Function • Families of discrete random variables • Cumulative distribution function (CDF) • Averages • Functions of a random variable • Expected value of a derived random variable • Variance and standard deviation • Conditional probability mass function

3 CONTINUOUS RANDOM VARIABLES • The cumulative distribution function • Probability density function • Expected values • Families of continuous random variables • Gaussian random variables • Delta functions, mixed random variables • Probability models of derived random variables • Conditioning a continuous random variable 4 PAIRS OF RANDOM VARIABLES • Joint cumulative distribution function • Joint probability mass function • Marginal PMF

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Joint probability density function Marginal PDF Functions of two random variables Expected values Conditioning by an event Conditioning by a random variable Independent random variables

10 STOCHASTIC PROCESS • Definitions and examples • Types of stochastic process • Random variables from random process • Independent, Identically distributed random sequences • Expected value and correlation • Stationary processes • Wide sense stationary stochastic processes • Cross-correlation 11 RANDOM SIGNAL PROCESSING • Linear filtering of a continuous-Time Stochastic process • Power spectral density of a continuous-time process • Cross spectral density • Frequency domain filter relationship References: Roy D. Yates, David J. Goodman, “Probability and Stochastic Process”, 2nd Edition, John Willey & Sons Inc, 2005. (Course Textbook) Peyton Z. Peebles, Jr., “Probability, Random Variables and Random Signal Principles”, 4th Edition, McGraw-Hill, New York, NY, 2001. Jorge I.Aunon and V.Chandrasekar, “Introduction to Probability and Random Processes”, McGraw-Hill, New York,1996. Henry Stark and John W.Woods, “Probability and Random Processes with applications to Signal Processing”, 3rd Edition, Prentice Hall,2002.

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INFORMATION/REMINDERS •

Tests would be expected in the middle and towards the end of the semester. Please note that the proposed date for TEST 1 is on the 25th January 2007(Friday night) while TEST 2 is on the 7st March 2007 (Friday). Students who have been paying attention during lecture and tutorial hours will be able to do well in the tests. Please also note that there will be no make up test if you miss any without valid proof.

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The lecturer has the right to give quizzes at any time she desires with/without prior notice. Hence, students are advised to be prepared at all time. There will be no make-up quiz if you miss any.

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There will be one comprehensive final exam at the end of the semester. The final examination will cover almost every topic in the course. Students who have been studying consistently through out the semester will be able to perform well in the exam.

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Students are expected to submit their assignments on time. Late submission without valid reason/proof will not be accepted.

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Attendance is compulsory. Students are required to sign an attendance sheet in every lecture and tutorial session. A letter will be sent by the department to the parents’ of the student who misses any lecture more than 3 times (whether it is 3 times in a row or not) without valid proof. A student must attend not less than 80% of the contact hours of the subject concerned. Student whose attendance is less than 80% may be barred from taking any form of assessment.

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There will be 1-hour tutorial a week in most weeks. The purpose of the tutorial is to go through assignments, quizzes and some other issues related to the course. I would really like to encourage students to regard this tutorial hour as your consultation hour where the students can have the advantage of asking the lecturer on any topics that the students may find it hard to understand during lectures. Students are expected to have gone through the tutorial questions meant for that week.

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Plagiarism in any form is not permitted. Students who are caught in any form of plagiarism will be penalized.

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Course Outcomes Course Outcomes 1. Illustrate and solve the concept of basic probability theories using tree diagram and set theory. 2. Identify, use and apply discrete random variable theory from given facts to solve electrical engineering and daily life problems. 3. Identify, use and apply continuous random variable theory from given facts to solve electrical engineering and daily life problems. 4. Identify and develop mixed random variable from given facts to solve electrical engineering and daily life problems. 5. Evaluate and analyze on pairs of random variables. 6. Predict the correlation and independence between random variables.

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7. Explain the concept and the use of random variables in stochastic process. 8. Evaluate and calculate the correlation of stochastic process. 9. Predict the behaviour of stochastic process being stationary or wide sense stationary.

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10. Apply the properties of wide sense stationary processes to solve the problem of random signal processing.

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3 – total fulfillment of PO with formal assessment 2 – partial fulfillment of PO with formal assessment 1 – related to PO without formal assessment

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Assessments Methods 1. Quiz 1 –Chapter 1 2. Quiz 2 –Chapter 2 3. Quiz 3-Chapter 3 4. Test 1- Chapter 1,2,3 5. Test 2-Chapter 4,10,11 6. Computer Assignment (using Matlab) 7. Final Exam

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