ECE 313
Section B (Tue/Thu)
Course Outline (Tentative)
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
Mini Project 1: Failure data analysis for Software-as-a-Service (SaaS) business application
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
Mini Project 2: Multi-parameter Signal Analysis for Patient Monitoring
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
Mini Project 3: Binary Hypothesis Testing for Real-time Patient Monitoring
VI. Joint Distributions
- Joint CFDs and PDFs
- Jointly Gaussian random variables
- Functions of many random variables
- Law of large numbers
- The Central Limit Theore
Final Project: Analysis of Performance and Reliability of Computer Systems
VI. Summary and Overview