In Class Demos

EE 364: Introduction to Probability and Statistics for EE/CS

Interactive notebooks for EE 364. Run locally or in JupyterLab.

Week 1: Introduction to Probability

• Randomness Demo — Can you fake randomness? Small-sample variability and statistical regularity.

Week 2: Conditioning and Independence

• Conditioning Demo — Simpson’s paradox and Berkson’s bias: phantom correlations from aggregation and selection.
• Binary Channel — Total probability, Bayes’ theorem, and channel capacity on the BSC.

Week 3: Counting and Discrete Distributions

• Counting Demo — Birthday collisions and derangements converging to \(1/e\).

Week 4: Discrete Distributions

• Discrete Explorer — Interactive PMF/CDF for the discrete BEG-CUP distributions.
• Geometric Waiting Times — Memoryless property, counterexample, and the coupon collector.
• Poisson Demo — Poisson as a binomial limit. The Poisson process and rare-event approximation quality.

Week 7: Continuous Distributions and Detection

• Continuous Explorer — Interactive PDF/CDF for continuous BEG-CUP distributions.
• Signal Detection — Hypothesis testing, ROC curves, \(d'\), and the \(\alpha\)/\(\beta\) tradeoff.
• Thick Tails — Gaussian vs Cauchy: why the sample mean doesn’t converge.

Week 9: Functions of Random Variables

• Density Transforms — How a PDF changes under \(Y = g(X)\), and the stretching factor \(|dx/dy|\).
• CDF Sampling — Generating draws from any distribution via \(F^{-1}\).