ECE 313 - F, Fall 2016, University of Illinois at Urbana-Champaign
ECE 313
PROBABILITY WITH ENGINEERING APPLICATIONS
Section G (Mon/Wed) - IYER
Spring 2017
Course Outline (Tentative)
Main Page
Course Outline
Grading Policies
Lectures
Homework Problems and Solutions
Student Projects
Resources
Exams
I. Introduction
Motivation
Course objectives/outline
Probability theory, models and their uses, examples
Definitions: sample space, elements, events
Algebra of events (union, intersections, laws/axioms)
Probability axioms and other useful relationships
Basic procedure for problem solving and an example
Combinatorial problems
Introduction to measurements
II. Conditional Probability and Independence of Events
Definitions of conditional problems, multiplication rule
Example
Independent events and associated rules
Application to reliability evaluation:
Series systems
Parallel redundancy
Example: series-parallel system evaluation
Theorem of total probability, Bayes' Formula
Examples:
Error-prone communication channel
Non-series-parallel system
Application to system reliability
III. Bernoulli Trials
TMR system with voter
Multiple failure modes
IV. Random Variables (Discrete)
Introduction: random variables and associated event space
Probability mass function
Special discrete random variables and their distribution:
Binomial
Geometric
Poisson
Uniform
Application to program/algorithmic analysis
Performance measurements using SPEC and other benchmarks
V. Random Variables (Continuous)
Mean, median, variance models
Distribution function, probability density function
Exponential distribution
Application to reliability evaluation
Memory less property and simple Markov model
Other important distributions:
Normal
Hyper and hypo exponentials
Weibull
Expectations:
Mean, median, variance, covariance, correlation
Expectation of function of random variables
Mean time to failure, Failure rates, and Hazard function
Conditional expectation
Inequalities and limit theorems
Fault coverage and reliability
More on performance and failure measurements and analysis
VI. Joint Distributions
Joint CFDs and PDFs
Jointly Gaussian random variables
Functions of many random variables
Law of large numbers
The Central Limit Theore
VI. Summary and Overview