ECE 313

• Core Curriculum

To develop an understanding of probabilistic phenomena in electronic systems with applications to reliability, system engineering, engineering decision-making, and parameter estimation.

• Probability spaces
• Conditional probability and independence
• Bayes' rule and decision making under uncertainty
• Reliability of systems
• Random variables
• Many random variables
• Applications
• Limit theorems

To develop an understanding of probabilistic phenomena in electronic systems with applications to reliability, system engineering, engineering decision-making, and parameter estimation.

Topics:

• Probability spaces
• Conditional probability and independence
• Basic probability distributions and how they arise
• Bayes' rule and decision making under uncertainty
• Reliability of systems
• Random variables
• Functions of random variables
• Many random variables (joint distributions, covarince, prediction, etc.)
• Applications
• Limit theorems

No required assignments; optional assignments may be given.

• Calculus
• Basic linear algebra

B. Hajek, Notes for ECE 313: Probability with Engineering Applications

Required for Computer Engineering and Electrical Engineering curricula.

Engineering Science: 3 credits

ECE 313 is a junior-level required course in both the EE and CompE curricula. The course introduces students to the theory of probability and its applications to engineering problems in the reliability of circuits and systems, and to statistical methods for hypothesis testing, decision-making under uncertainty, and parameter estimation. The goal is to provide the student with an adequate knowledge of probability and probabilistic reasoning in engineering analyses, and of statistical methods to enable the student to apply these techniques in advanced senior-level elective courses. The course serves as a prerequisite or co-requisite for advanced undergraduate-level technical electives in the areas of signal processing, computer networks, and communications such as

• ECE 365 - Data Science and Engineering
• ECE 461 - Digital Communications
• ECE 418 - Image and Video Processing
• ECE 438 - Communication Networks
• ECE 459 - Communications I
• ECE 463 - Digital Communications Laboratory

as well as numerous graduate courses.

At the end of this course, the student will be able to apply the knowledge of probability and statistics gained in this course to several different types of problems in engineering.

1. Given a network of hosts that communicate with each other over links that are prone to failure, the student will be able to compute the probability that there exists a viable communication path between any two nodes in the network. (1) The student will also be able to model failure modes for systems composed of several subsystems as a network problem, and to solve such problems. (1)

2. The student will be able to formulate engineering decision-making problems as hypothesis testing schemes that compare likelihood ratios to thresholds. (1, 2) The student will be able to calculate the thresholds required to meet design specifications such as maximum false-alarm probabilities or detection probabilities in radar decision problems. (1,6) The student will be able to design tests using Bayesian methods for the purpose of minimizing the average probability of error. (1,2)

3. The student will be able to specify maximum-likelihood estimates for system parameters. (1,2,6) The student will be able to estimate confidence intervals for parameters for any specified confidence level. (1)

4. The student will be able to compute probability distributions for the parameters of various systems, to estimate average values and variances of these parameters, and to estimate the probabilities that various design specifications are met. (1,6)