Undergraduate/graduate course introducing probability and statistical inference with a strong emphasis on data science applications, computation in R (and Python), and modern inferential tools.
Course Overview and Motivation
Probability Basics
Monte Carlo Methods: Introduction
Random Variables, Mean, and Variance
Variance, Covariance, and Dependence
Discrete Distributions
Continuous Distributions
Statistical Basics and Empirical Distributions
Fitting Continuous Models
The Normal Distribution
Introduction to Statistical Inference
Multivariate Distributions
Probability Basics:
Typed notes
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Handwritten notes
Random Variables:
Typed notes
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Handwritten notes
Multivariate Distributions:
Typed notes
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Handwritten notes
Conditional Distributions and Moments:
Typed notes
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Handwritten notes
Continuous Distributions:
Typed notes
Random Variable Convolutions:
Typed notes
Random Sampling:
Typed notes
Stochastic Processes and Markov Chains:
Handwritten notes
Statistical Inference (Basics):
Handwritten notes
Confidence Intervals:
Handwritten notes
Parametric Inference:
Handwritten notes
Hypothesis Testing:
Handwritten notes
Permutation & KS Tests:
Typed notes
Bootstrap:
Typed notes
Likelihood Ratio Tests:
Typed notes
When both typed and handwritten notes are available, they offer complementary perspectives on the same material.
Homework assignments emphasize conceptual understanding, analytical reasoning, and computation in R. Selected solution files and source materials are available upon request.
These materials are provided for practice and illustration purposes only.
The code repositories include illustrative scripts and notebooks used throughout the course, covering probability simulations, Monte Carlo methods, resampling, Markov chains, regression, and related computational topics.
The code provided here was developed for instructional purposes and reflects working implementations used in this course. While these scripts ran correctly in the instructor’s environment, no guarantee is made regarding correctness, efficiency, or suitability for other settings. Users are encouraged to adapt and validate the code for their own purposes. If you notice any errors, inconsistencies, or opportunities for improvement, I would greatly appreciate being contacted so that corrections can be made.
These notes are provided as optional background references to support probability and statistics concepts used in the course.
Materials are provided for educational use. While care has been taken in their preparation, errors or omissions may occur. If you notice any errors, inconsistencies, or ambiguities in the lecture notes, homework problems, or sample exams, I would appreciate being contacted so that corrections can be made. Please contact me before reuse or adaptation.