ECE 313



I. Foundations of Probability

  1. Axioms of Probability Theory
  2. Basic set theory
  3. Countably infinite sets

II. Discrete-Type Random Variables

  1. Random variables and probability mass functions
  2. Mean and variance of a random variable
  3. Conditional probabilities and independence
  4. Markov and Chebyshev inequalities
  5. Some important examples
  6. Bayes formula and the law of total probability
  7. Maximum-likelihood (ML) rule
  8. Binary hypothesis testing
  9. Reliability theory

III. Continuous-Type Random Variables

  1. Cumulative distribution functions (CDFs) and probability density functions (pdf's)
  2. Important examples
  3. The Gaussian distribution
  4. Functions of random variables
  5. Expectation of a function of a random variable
  6. Conditional distributions
  7. Reliability, hazard (failure) rates

IV. Joint Distributions of Random Variables

  1. Joint CDFs and pdfs
  2. Covariance and correlation
  3. Jointly Gaussian random variables
  4. Sums of random variables
  5. Other functions of many random variables
  6. Law of large numbers
  7. The Central Limit Theorem