STAT 4843 - Theory of Probability
Fall 2026 Syllabus, Section 01, CRN 43606,
Credit hours: 3
Course Meeting Times
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Instructor
Lucy Kerns
Email: xlu@ysu.edu
Course Description
4843. Theory of Probability. The mathematical foundation of probability theory including the study of discrete and continuous distributions. Other topics selected from limit theorems, generating functions, stochastic processes, and applications. Prereq.: STAT 3743 and one of MATH 2673 or MATH 2686H or consent of department chairperson. 3 s.h.
Course Readings
| Group | Title | Author | ISBN |
|---|---|---|---|
| Required | Statistical Inference (2nd Edition) | George Casella and Roger L. Berger. | 978-0534243128 |
The course readings are subject to change in the event of extenuating circumstances, research developments, current events, and/or to ensure better learning.
Assignments/Assessments
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Schedule of Topics and Assignments
| Week of | Reading(s) | Proposed Topic | Due/To Prepare for Class |
|---|---|---|---|
| 8/25 | Section 1.1 Set Theory | Sample space,events, set operations, basic laws of set theory, partition of sample space | |
| 9/1 | Section 1.2 Basics of Probability Theory | Sigma-algebra, probability function, counting techniques | Quiz 1 |
| 9/8 | Section 1.3 Conditional Probability and Independence | Conditional probability, independent events, Bayes' rule | Quiz 2 |
| 9/15 | Section 1.4 Random Variables and Distributions | Random variables, cumulative distribution function, density and mass function | Quiz 3 |
| 9/22 | Section 2.1 Distributions of Functions of a Random Variable | Distributions of functions of discrete and continuous random variables | Exam 1 |
| 9/29 | Section 2.2 Expected Values | Definition and properties of expectations | Quiz 4 |
| 10/6 | Section 2.3 Moments and Moment Generating Functions | Defintion and properties of moments and moment generating functions | Quiz 5 and Exam 2 |
| 10/13 | Section 3.1 Discrete Distributions | Uniform, Hypergeometric, and Binomial distributions | Quiz 6 |
| 10/20 | Section 3.1 Discrete Distributions | Poisson, Negative Bionomial, and Geometric distributions | |
| 10/27 | Section 3.2 Continuous Distributions | Uniform, Normal and Gamma distributions | Quiz 7 |
| 11/3 | Section 3.2 Continuous Distributions | Exponential and Beta Distributions | Exam 3 |
| 11/10 | Section 4.1 Joint and Marginal Distributions | Joint and marginal probability mass function, joint and marginal probability density function | Quiz 8 |
| 11/17 | Section 4.2 Conditional Distributions and Independence | Conditional distribution and independence of two random variables | Quiz 9 |
| 11/24 | Section 4.3 Bivariate Transformation | One-to-One and Two-to-One bivariate transformations | Quiz 10 |
| 12/1 | Section 4.4 Hierarchical Models and Mixture Distributions; Section 4.5 Covariance and Correlation | Hierarchical models, defintion and properties of covariance and correlation | |
| 12/8 | Finals Week | Final Exam |
The course schedule, policies, procedures, and assignments in this course are subject to change in the event of extenuating circumstances, by mutual agreement, and/or to ensure better learning.