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.

Course Description

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.

Prerequisites

((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.

Textbook

A First Course in Probability by Sheldon Ross, 10th edition

Course Schedule and Slides

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