A Quick Refresher on Analysis and Probability
Abstract
Most of the material in this chapter is from basic analysis and probability courses. Key concepts and results are recalled here, including convexity, norms and inner products, random variables and random vectors, union bound, conditioning, basic inequalities (Jensen, Minkowski, Cauchy–Schwarz, Hölder, Markov, and Chebyshev), the integrated tail formula, the law of large numbers, the central limit theorem, normal and Poisson distributions, and handy bounds on the factorial.
Fields of Study & Subjects
Probability and Statistical Research
Statistical Methods and Applications
Point processes and geometric inequalities
Publication details
- Journal / source
- Cambridge University Press eBooks
- Pages
- 8–23
- Publication date
- 30 January 2026
- Document type
- Book chapter