AI Tutor Prompts for Probability, Statistics, and Stochastic Processes:A Companion to the Graduate Course Notes

Abstract

AI Tutor Prompts for Probability, Statistics, and Stochastic Processes: A Companion to the Graduate Course Notes Paste-ready prompts for a generic large-language-model assistant used with the graduate course companion Probability, Statistics, and Stochastic Processes. The file covers the thirteen-chapter sequence: probability spaces and σ\sigmaσ-algebras, conditioning and independence, random variables, concentration inequalities, random vectors, conditional expectation and modes of convergence, stochastic processes and inference, Markov and renewal models, Brownian motion and martingales, PCA and likelihood, paired tests, bootstrap and annealing, and information theory as an application of those objects. Each chapter has four prompts—Background, Introductory, Tutorial, and Advanced—plus a project brief that fixes notation (Ω,F,P)(\Omega,\mathcal F,\mathbb P)(Ω,F,P) and the examinable core. The assistant is a tutor, not a substitute for the companion, the solutions notebook, or canonical texts (Durrett, Williams, Cover and Thomas, Casella and Berger). This work is part of the same record as the course companion. Licence: CC BY 4.0. Errata: jose.tamezpena@tec.mx.