MAT5373
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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 | ||
