12-Probability and Statistics

Overview

This textbook develops foundational and advanced methods in probability theory and statistical inference. Topics include random variables, distributions, expectation, estimation, hypothesis testing, regression, and stochastic processes, with emphasis on real-world data modeling.

Table of Contents

1. Chapter 1: Probability and Statistics Overview
2. Chapter 2: Probability Rules
3. Chapter 3: Discrete Random Variables
4. Chapter 4: Continuous Random Variables
5. Chapter 5: Joint Distributions
6. Chapter 6: Transformations, Expectation, and Moment Methods
7. Chapter 7: Limit Theorems
8. Chapter 8: Estimation and Confidence Intervals
9. Chapter 9: Hypothesis Testing
10. Chapter 10: Likelihood and Bayesian Methods
11. Chapter 11: Linear Regression
12. Chapter 12: Multiple Regression and ANOVA
13. Chapter 13: Stochastic Processes
14. Chapter 14: Advanced Topics in Probability and Statistics
15. Back Matter

Learning Outcomes

• Apply probability rules to compute and interpret uncertainties.
• Analyze discrete and continuous random variables and distributions.
• Compute expectations, variances, and higher moments.
• Perform statistical inference using estimation and hypothesis testing.
• Apply regression models to real-world data.
• Use Bayesian and likelihood-based reasoning for inference.
• Understand stochastic processes and time-dependent randomness.