ECE 313 - F, Fall 2016, University of Illinois at Urbana-Champaign

ECE 313


Section G (Mon/Wed) - IYER

Spring 2017

Course Outline (Tentative)

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Course Outline

Grading Policies


Homework Problems and Solutions

Student Projects



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:
  5. Theorem of total probability, Bayes' Formula
  6. Examples:

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:
  4. Application to program/algorithmic analysis
  5. Performance measurements using SPEC and other benchmarks

V. Random Variables (Continuous)

  1. Mean, median, variance models
  2. Distribution function, probability density function
  3. Exponential distribution
  4. Application to reliability evaluation
  5. Memory less property and simple Markov model
  6. Other important distributions:
  7. Expectations:
  8. More on performance and failure measurements and analysis

VI. Joint Distributions

  1. Joint CFDs and PDFs
  2. Jointly Gaussian random variables
  3. Functions of many random variables
  4. Law of large numbers
  5. The Central Limit Theore

VI. Summary and Overview