Department of Electrical and Computer Engineering

ECE 313



Course Outline (Tentative)

I. Introduction

  1. Motivation
  2. Course objectives/outline
  3. Probability theory, models and their uses, examples
  4. Definitions: sample space, elements, events
  5. Algebra of events (union, intersections, laws/axioms)
  6. Probability axioms and other useful relationships
  7. Basic procedure for problem solving and an example
  8. Combinatorial problems
  9. Introduction to measurements

II. Conditional Probability and Independence of Events

  1. Definitions of conditional problems, multiplication rule
  2. Example
  3. Independent events and associated rules
  4. Application to reliability evaluation:
    • Series systems
    • Parallel redundancy
    • Example: series-parallel system evaluation
    • Theorem of total probability, Bayes' Formula
  5. Examples:
    • Error-prone communication channel
    • Non-series-parallel system
  6. Application to system reliability
  7. Preliminary performance /reliability measurements in-lab and on a campus system

III. Bernoulli Trials

  1. TMR system with voter
  2. Multiple failure modes

IV. Random Variables (Discrete)

  1. Introduction: random variables and associated event space
  2. Probability mass function
  3. Special discrete random variables and their distribution:
    • Binomial
    • Geometric
    • Poisson
    • Uniform
  4. Application to program/algorithmic analysis
  5. Performance measurements using SPEC and other benchmarks
  6. Preliminary project presentations

V. Random Variables (Continuous)

  1. Mean, median, variance models
  2. Distribution function, probability density function
  3. Exponential distribution
  4. Application to reliability evaluation
  5. Other important distributions:
    • Normal
    • Hyper and hypo exponentials
    • Weibull
  6. Expectations:
    • Mean, median variance
    • Expectation of function of random variables
    • Mean time to failure
    • Conditional expectation
    • Inequalities and limit theorems
    • Fault coverage and reliability
  7. Final project presentations

VI. Summary and Overview