ECE ILLINOIS

ECE 313

PROBABILITY WITH ENGINEERING APPLICATIONS

COURSE SYLLABUS

I. Approaches to Probability

  1. Subjective, classical, and relative frequency approaches to probability
  2. The axiomatic approach to probability
  3. Consequences of the axioms and examples
  4. Use of Venn diagrams and Karnaugh maps
  5. Principle of inclusion and exclusion

II. Conditional Probability

  1. Definition of conditional probability; chain rule
  2. Theorem of total probability
  3. Bayes' formula and its use
  4. Bayes rule for deciding among competing hypotheses
  5. Maximum-likelihood (ML) rule
  6. Type I and Type II errors

III. Independence and Independent Trials

  1. Stochastic independence of two events
  2. Independence of multiple events
  3. Reliability of systems and networks
  4. Independent experiments and repeated independent trials

IV. Random Variables

  1. Definition
  2. Cumulative distribution function of a random variable
  3. Discrete and continuous random variables
  4. Mean and variance; mean, mode and median as measures of location
  5. Markov's inequality
  6. Chebyshev's inequality; variance as a measure of spread
  7. Examples of discrete and continuous random variables
  8. Functions of random variables
  9. Expectation of a function of a random variable
  10. Conditional distributions
  11. Reliability and hazard rates
  12. Hypothesis testing
  13. Maximum-likelihood estimation of parameters of distributions

V. Many Random Variables

  1. Joint distributions
  2. Covariance and correlation
  3. Jointly Gaussian random variables
  4. Sums of random variables
  5. Other functions of many random variables
  6. Linear regression

VI. Limit Theorems

  1. Weak law of large numbers
  2. Central limit theorem