Please note the official course website is on Canvas (log in with CNetID), NOT here. This webpage is for those who are interested in STAT 25100 to get an idea of what the course is like.
This course covers fundamentals and axioms; combinatorial probability; conditional probability and independence; binomial, Poisson, and normal distributions; the law of large numbers and the central limit theorem; and random variables and generating functions.
((MATH 16300/MATH 16310/MATH 20300/MATH 20310/MATH 20700), with no grade requirement), or (MATH 18400 or (MATH 15250 and 15300)) with (either a minimum grade of B-, or STAT major, or currently enrolled in prerequisite course during preregistration. Or instructor consent.
A First Course in Probability by Sheldon Ross, 10th edition
Week/Date | Slides | Content | Textbook Coverage
| Week | Date | Slides | Content | Textbook Coverage |
|---|---|---|---|---|
| 1 | June 16,18 | L01 | Syllabus; The Multiplication Rule for Counting; Permutations; Combinations; Combinatorial identities; Multinomial coefficients | 1.1-1.5 |
| 1 | W, June 18 | L02 | Sample Space, Events, Empty Set, Union, Intersection, Complement, Venn Diagram, De Morgan’s Law | 2.2 |
| 1 | F, June 20 | L03 | Axioms of Probabilities, Some Probability Rules; Sample Space with Equally Likely Outcomes | 2.3-2.5 |
| 2 | M, June 23 | L04 | Inclusion-Exclusion Formula; Conditional Probability | 2.4-2.5 |
| 2 | W, June 25 | L05 | Conditional Probability; Multiplication Rule | 3.2 |
| 2 | F, June 27 | L06 | Law of Total Probability; Bayes Rule; Independence of Events | 3.3, 3.4 |
| 3 | M, June 30 | L06 | Independence of Events | 3.4 |
| 3 | M, June 30 | L07 | Discrete Random Variables, Bernoulli & Binomial | 4.1, 4.2, 4.6 |
| 3 | W, July 2 | L07 | Geometric, Negative Binomial, Hypergeometric, Poisson Distributions | 4.7, 4.8 |
| 3 | F, July 4 | |||
| 4 | M, July 7 | L07 | Coupon Collector’s Problem | 4.1 |
| 4 | M, July 7 | L08 | Expected Values and Variances of Discrete Random Variables | 4.3-4.5 |
| 4 | W, July 9 | L08 | Factorial Moments of Discrete Random Variables | 4.3-4.5 |
| 4 | W, July 9 | L09 | Law of Small Numbers for the Poisson Distributions | 4.7 |
| 4 | F, July 11 | L10_11 | Continuous Random Variables (PDF, CDF) | 5.1 |
| 5 | M, July 14 | In-Class Midterm, 6-7:30 pm, proctored on Zoom | ||
| 5 | W, July 16 | L10_11 | Continuous Distributions (Normal, Exponential, Gamma, etc), Transformation of One Continuous Random Variable | 5.3-5.7 |
| 5 | F, July 18 | L10_11 | Various Normal Approximations | |
| 5 | F, July 18 | L12 | Expected Value & Variance of Continuous Random Variables; Hazard Rate Functions | 5.2 |
| 6 | M, July 21 | L13 | Joint & Marginal Distributions of Discrete & Continuous Random Variables, Independent Random Variables | 6.1-6.2 |
| 6 | W, July 23 | L13 | Independent Random Variables | 6.2 |
| 6 | W, July 23 | L14 | Conditional Distributions | 6.4-6.5 |
| 6 | F, July 25 | L15 | Sum of Random Variables; Transformation of 2+ Random Variables (Jacobian) | 6.3, 6.7 |
| 7 | M, July 28 | L15 | Order Statistics | 6.6 |
| 7 | M, July 28 | L16_17 | Expected Value of Functions of Random Variables; Covariance | 7.1-7.2, 7.4 |
| 7 | W, July 30 | L16_17 | Expected Value & Variance of Sum of Random Variables, Correlation | 7.4 |
| 7 | F, Aug 1 | L18 | Conditional Expectation, Conditional Variance, Tower Laws of Conditional Expectation and Conditional Variances | 7.5 |
| 8 | M, Aug 4 | L19 | Moment Generating Functions | 7.7 |
| 8 | M, Aug 4 | L20 | Chebyshev Inequality, Weak Law of Large Numbers, Central Limit Theorem | 8.2-8.3 |
| 8 | W, Aug 6 | L21 | Summary & Review | |
| 8 | F, Aug 8 | In-Class Final, 6-8 pm, proctored on Zoom |