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ECE 313

PROBABILITY WITH ENGINEERING APPLICATIONS

COURSE SYLLABUS

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I. Foundations of Probability

- Axioms of Probability Theory
- Basic set theory
- Countably infinite sets

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II. Discrete-Type Random Variables

- Random variables and probability mass functions
- Mean and variance of a random variable
- Conditional probabilities and independence
- Markov and Chebyshev inequalities
- Some important examples
- Bayes formula and the law of total probability
- Maximum-likelihood (ML) rule
- Binary hypothesis testing
- Reliability theory

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III. Continuous-Type Random Variables

- Cumulative distribution functions (CDFs) and probability density functions (pdf's)
- Important examples
- The Gaussian distribution
- Functions of random variables
- Expectation of a function of a random variable
- Conditional distributions
- Reliability, hazard (failure) rates

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IV. Joint Distributions of Random Variables

- Joint CDFs and pdfs
- Covariance and correlation
- Jointly Gaussian random variables
- Sums of random variables
- Other functions of many random variables
- Law of large numbers
- The Central Limit Theorem