Study guide for Probability Theory (35B115-B-3) at Tilburg University, covering lectures 1-10 with full proofs and explanations. Topics include random variables, distributions (discrete and continuous), joint distributions, independence, covariance, conditional expectation, and transformations, all aligned with course slides and notation. Structured for exam success with clear identification of theorems, common pitfalls, and practice problems—saves time by consolidating lecture material and te...