CEN 343 Syllabus
INTRODUCTION TO RANDOM PROCESSES
Lecture: Sunday-Thursday-Tuesday 1:00-1:50
Tutorial: Thursday 3:00-3:50
Office hours: ALISR Laboratory
Course Description:
Covers probability theory, random variables, descriptive statistics, random sampling, statistical intervals and hypothesis testing for a single sample, stochastic processes, spectral characteristics and applications to systems
Textbook(s) and/or Other Required Materials:
Peebles, P., Probability, Random Variables and Random Signal Processing, 4th Ed., 2001, McGraw Hill.
Sullivan III, M., Statistics: Informed Decisions Using Data, 3rd Edition, 2010, Pearson.
Course Learning Outcomes:
This course requires from the student to demonstrate the following:
1. Explain basic concepts probability, joint probability, conditional probability, independence, total probability, and Bayes’ rule.
2. Define random variables in terms of their PDF and CDF, and some distributions
3. Calculate the mean, variance, and joint moment of two random variables such as the correlation and covariance.
4. Define random sampling, data, and understand the central limit theorem
5. Explain important properties of point estimators: unbiased, minimum variance, and mean square error
6. Construct point estimators using maximum likelihood
7. Construct confidence intervals on mean of a normal distribution for variance known and unknown
8. Construct confidence intervals on the variance and standard deviation of a normal distribution
9. Test binary hypotheses on the mean of a normal distribution with variance known and unknown
10. Determine if a random process is wide sense stationary, stationary, and ergodic.
11. Calculate the mean, variance, autocorrelation, and power spectral density of a stationary random process such as the additive white Gaussian noise process.
Major Topics covered and schedule in weeks:
Set theory and probability basics: 2
Random variables and some distributions: 2
Two dimensional random variables: 2
Statistics: 4
Stochastic processes and spectral characteristics: 3
Review and evaluation: 2
Evaluation
Attendance: 5%
Assignments: 10%
Quizzes: 15%
Two Midterm exams: 30%
Final exam: 40%