ECE 313
Section X (Tue/Thu)
Course Outline (Tentative)
I. Probability Theory Basics
- 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
II. Conditional Probability, Independence of Events, and Bernoulli Trials
- Definitions of conditional probability, Bayes rule
- Theorem of total probability and Bayes Formula
- Independent events and associated rules
- Independence vs. Mutual exclusivity
Mini Project 1: Analysis of alarms data from ICU patient monitoring systems
- Bernoulli Trials
- Reliability evaluation applications:
- Series systems
- Parallel redundancy
- Series-parallel system evaluation
- Non-series-parallel systems
- Triple Modular Redundant (TMR) system with voter
III. Random Variables (Discrete)
- Introduction to random variables and associated event space
- Cumulative distribution function (CDF)
- Probability mass function
- Important discrete random variables and their distributions:
- Bernoulli and Binomial
- Geometric and modified geometric
- Poisson
IV. Random Variables (Continuous)
- Probability density function (PDF)
- Important continuous random variables and their distributions:
- Uniform
- Gaussian (Normal)
- Exponential
Mini Project 2
V. Exponential Distribution
- Memory-less property
- Relationship to Poisson distribution and examples
- Phase-type exponential distributions:
- Hypo-exponentials
- K-stage Erlang
- Gamma
- Hyper-exponential
- Applications to reliability evaluation
VI. Expectations:
- Moments: Mean and variance
- Mean and variance of important random variables
- Conditional expectation
- Expectation of function of random variables
- Covariance and correlation
- Reliability evaluation applications:
- Mean time to failure
- Failure rates
- Hazard functions
- Failure Data Analysis
Final Project: Analysis of Performance and Reliability of Computer Systems
VII. Joint and Conditional Density Functions
- Joint CFDs and PDFs
- Jointly Gaussian random variables
- Functions of many random variables
- Independent random variables
VIII. Binary Hypothesis Testing
IX. Inequalities and Limit Theorems
Markov Inequality
Chebyshev’s inequality
Law of large numbers
The Central Limit Theorem