# Mathematical Foundations of Statistics I - MAT4173/5373

Catalog entry

Prerequisite: MAT1213/MAT1214 Calculus I.

Content: Mathematical Foundations of Statistics I is an introductory course that covers key concepts in statistics from a mathematical perspective, including populations and samples, descriptive statistics, probability, discrete and continuous distributions, transformations, jointly distributed random variables, covariance and correlation, order statistics, and the Central Limit Theorem. The course equips students with foundational knowledge and techniques for data analysis and statistical modeling in various fields.

## List of Topics

 Session Section Topic Pre-requisites 1 1.1 Populations and Samples 2 1.2 Pictorial and Tabular Methods in Descriptive Statistics 3 1.3 Measures of Location 4 1.4 Measures of Variability 5 2.1 Sample Spaces and Events 6 2.2 Axioms, Interpretations, and Properties of Probability 7 2.3 Counting Techniques 8 2.4 Conditional Probability 9 2.5 Independence 10 REVIEW 11 TEST 1 12 3.1 Random Variables 13 3.2 Probability Distributions for Discrete Random Variables 14 3.3 Expected Values of Discrete Random Variables 15 3.4 Moments and Moment Generating Functions 16 3.5 The Binomial Probability Distribution 17 3.6 Hypergeometric and Negative Binomial Distributions 18 3.7 The Poisson Probability Distribution 19 4.1 Probability Density Functions and Cumulative Distribution Functions 20 4.2 Expected Values and Moment Generating Functions 21 4.3 The Normal Distribution 22 4.4 The Gamma Distribution and Its Relatives 23 4.5 Other Continuous Distributions 24 4.6 Probability Plots 25 4.7 Transformations of a Random Variable 26 REVIEW 27 TEST 2 28 5.1 Jointly Distributed Random Variables 29 5.2 Expected Values, Covariance, and Correlation 30 5.3 Conditional Distributions 31 5.4 Transformations of Random Variables 32 5.5 Order Statistics 33 6.1 Statistics and Their Distributions 34 6.2 The Distribution of the Sample Mean 35 6.3 The Mean, Variance, and MGF for Several Variables 36 6.4 Distributions Based on a Normal Random Sample 37 6.5 Proof of the Central Limit Theorem 38 REVIEW