This repository contains my lecture notes and solved problems from Casella-Berger: Statistical Inference (Chapters 1-5), focused on foundational concepts in Probability Theory and Statistical Inference. These topics are essential for Machine Learning, AI, and Robotics.
- Probability Theory: Set theory, Cardinality & Countability, Probability Spaces, Borel sets, and Lebesgue measure.
- Transformations and Expectations: Distributions of functions, Moment-Generating Functions.
- Common Families of Distributions: Discrete and Continuous distributions, Exponential families, Inequalities.
- Multiple Random Variables: Joint and marginal distributions, conditional distributions, mixture models.
- Properties of a Random Sample: Sample mean, variance, order statistics, convergence, and random sampling.
- Lecture Notes: Theoretical concepts and theorems.
- Problem Sets: Solutions to exercises from Casella-Berger for reinforcing understanding.
| Chapter | Topics |
|---|---|
| Ch1 — Probability Theory | cardinality & countability, probability spaces, Borel sets & Lebesgue measure, conditional probability & independence, random variables & CDFs |
| Ch2 — Transformations & Expectations | transformations of random variables, expectation & moments, PGFs and MGFs |
| Ch3 — Common Families of Distributions | discrete & continuous families, Bernoulli / Poisson processes, exponential families, Markov & Chebyshev inequalities |
| Ch4 — Multiple Random Variables | joint / marginal / conditional distributions, bivariate transformations, hierarchical & mixture models, covariance & correlation |
| Ch5 — Properties of a Random Sample | random samples, sampling from the normal, order statistics, convergence concepts |
Most chapters have an *_Exercises_Solutions/ subfolder of solved Casella-Berger problems; see also Miscellaneous_Topics.
These notes and solutions reflect my attempt to solidify my mathematical skills and understanding. I aim to build a strong theoretical foundation in Statistical Inference, which will support my future work in Machine Learning, AI, and Robotics research.
When I have the opportunity, I hope to document my notes and solutions in LaTeX for better clarity and organization.
A sequence building from mathematical foundations toward machine-learning applications:
- Real Analysis
- Probability and Distribution Theory — this repo
- Statistical Inference Theory
- Reinforcement Learning
I am focused on building a strong theoretical foundational math skill, which will be crucial for my future work in Robotics research.
Feel free to reach out:
- Email: sampath@umich.edu
- LinkedIn: www.linkedin.com/in/sai-sampath-kedari