MAT5373

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