Part IV — Random Vectors, Limit Theorems, and Stochastic Processes

Booklet: Abridged Math Foundations for Signal Processing, Machine Learning, and Artificial Intelligence, Lessons 18–23 (PDF).

Derived distributions, covariance, and correlation; conditional expectation and least-mean-squares estimation; random vectors and Gaussian vectors; limit theorems; the Bernoulli and Poisson processes; Markov chains.

24 exercises across Lessons 18–23 — 12 [Hand], 12 [Proof].

Exercises

Worked sets are linked below as they are completed.

• Lesson 18 — Derived Distributions, Covariance, and Correlation — 4 exercises (2 [Hand], 2 [Proof])
• Lesson 19 — Conditional Expectation and Least Mean Squares — 4 exercises (2 [Hand], 2 [Proof])
• Lesson 20 — Random Vectors and Gaussian Vectors — 4 exercises (2 [Hand], 2 [Proof])
• Lesson 21 — Limit Theorems — 4 exercises (2 [Hand], 2 [Proof])
• Lesson 22 — The Bernoulli and Poisson Processes — 4 exercises (2 [Hand], 2 [Proof])
• Lesson 23 — Markov Chains — 4 exercises (2 [Hand], 2 [Proof])