Course Prefix and Number:
TE 3341

Credits:
3 Hours

Prerequisites:
MATH 1472 (Calculus II)

Semester and Year:
Fall 1999

Instructor:
Dr. Philip C. Loizou

Class Time:
Monday and Wednesday

8:30-9:45 pm / GR 2.508

Office Location:
EC 2.512

Office Hours:
MW 4:00-5:00 pm, TR 11:00-12:00 or by appointment

E-mail:
l[email protected]

**COURSE OBJECTIVE**

To introduce the fundamentals of probability theory and random processes and illustrate these concepts with engineering applications. This course will present the basic principles of random variables and random processes needed in applications such as signal processing, digital communications, speech processing, data modeling, etc. MATLAB will be used as a software tool for bringing probability theory and real-world applications closer together.

**TEXTBOOK**

D. Childers (1997). *Probability and Random
Processes*, WCB/McGraw Hill.

Download MATLAB software for the course.

**ASSIGNMENTS & GRADING**

The course requirements consist of:

- homework assignments, and computer assignments
- one MATLAB computer project
- two in-class exams and one final exam (comprehensive).

- Homework and computer assignments: 35%
- Project : 15%
- Exams : 30% (2x15)
- Final Exam : 20%

**POLICIES**

- Homework may be turned in one class after it is due with a late penalty of 10%. Homework will not be accepted more than one class day late.
- Make-up exams will not be given without advance notice to the instructor.

Please see the UTD Graduate catalog for policy on academic dishonesty. Giving or receiving aid on a graded assignment or test is considered cheating and will be harshly penalized.

**TOPICS**

- Introduction (Chap. 1)

- Set theory
- Functions

- Introduction to Probability Theory (Chap. 2)

- The sample space (discrete and continuous)
- Probability function
- Events
- Axioms of probability
- Conditional probabilities
- Independent events

- Random variables (Chap. 3)

- Probability distribution functions for discrete random variables
- Cumulative probability distribution and probability density functions
- Examples of probability density functions (Gaussian, uniform, etc.)
- Joint probability density functions

- Conditional probability density and distribution functions
- Statistical independence
- Vector random variables

- Expectation (Chap. 4)
- Moments
- Expectation of a function of a random variable
- Characteristic function
- Expectation of random vectors
- Central limit theorem

- Random processes (Chap. 5)
- Random processes and ensembles
- Examples of random processes

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