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

Booklet: Abridged Math Foundations for Signals and Systems, Lessons 21–27 (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 21–26 — 12 [Hand], 12 [Proof]. Lesson 27 is Capstone IV (a project, no exercise block).

Exercises

Worked sets are linked below as they are completed.

• Lesson 21 — Derived Distributions, Covariance, and Correlation — 4 exercises (2 [Hand], 2 [Proof])
• Lesson 22 — Conditional Expectation and Least Mean Squares — 4 exercises (2 [Hand], 2 [Proof])
• Lesson 23 — Random Vectors and Gaussian Vectors — 4 exercises (2 [Hand], 2 [Proof])
• Lesson 24 — Limit Theorems — 4 exercises (2 [Hand], 2 [Proof])
• Lesson 25 — The Bernoulli and Poisson Processes — 4 exercises (2 [Hand], 2 [Proof])
• Lesson 26 — Markov Chains — 4 exercises (2 [Hand], 2 [Proof])
• Lesson 27 — Capstone IV: Estimation and Simulation in NumPy — project