| Instructor: | Dr. Kristine Bell | Office: | S&T II, Rm. 145 | |
| email: | kbell@gmu.edu | Phone: | (703)-993-1707 |
| Time: | Wed. 4:30-7:10 p.m. |
| Place: | Innovation Hall, Rm. 133 |
| Office Hours: | Tues. 3:00-4:00 p.m., 7:30-8:00 p.m. or by appointment |
| Final Exam: | Wed. 5/7/08, 4:30-7:15 p.m. |
The following information is provided to give a general idea of STAT 544 course structure and policies when taught by Prof. Bell. Details about policies, schedules, assignments, and exams for a given semester will be provided to students registered for the class in a semester-specific syllabus and on Blackboard.
Prerequisites: MATH 213 (Multivariable Calculus) and STAT 344 (calculus-based Probability).
Text: Sheldon Ross, A First Course in Probability, 7th ed., Prentice-Hall, 2006. (black cover)
Description: This course presents the mathematical framework of applied probability theory. It is a calculus-based course with emphasis on developing probability concepts and problem solving skills with applications in computer science, engineering, operations research, and statistics. Topics covered include combinatorics, probability axioms, conditional probability and independence, random variables, expectation, moment generating functions, transformations of random variables, special discrete and continuous distributions, jointly distributed random variables, sums of random variables, and limit theorems.
This course builds on the probability concepts studied at the undergraduate level, with more emphasis placed on advanced topics and derivations of key results.
Grading: Grades are based five components: Weekly Homework, Weekly Quizzes, In-class Midterm Exam, In-Class Final Concept Quiz, and In-class Final Exam.
Blackboard: Course materials, announcements, etc. will be disseminated through Blackboard.
Frequently Asked Questions: Frequently Asked Questions, Homework #0
Topics Covered:
| Lecture | Topics | Sections | Representative Problems |
| 1 | Review of Set Theory, Sample Spaces and Events, Probability Axioms and Laws | 2.1-2.5 | 2P: 8, 10, 13, 23, 24, 33, 35, 37, 38 2 T: 11, 12, 16 |
| 2 | Counting Techniques | 1.1-1.5 | 1P: 4, 8, 10, 16, 20, 21, 22, 27, 28 1T: 13 |
| 3 | Conditional Probability and Independence | 3.1-3.5 | 3P: 4, 5, 9, 12, 16, 18, 21, 23, 55, 66(a) 3T: 1, 5(a), 9, 25 |
| 4 | Discrete RVs: PMF, CDF, Probability, transformation of RV, Expected Value | 4.1-4.3, 4.9 | 4 P: 1, 4, 7(a,b), 8(a,b), 18, 19, 21(b), 28, 35(a) |
| 5 | Mean, Variance, Standard Deviation; Properties of Expectation; Markov's, Chebyshev’s, and Jensen's Inequalities; Moments and Moment Generating Function | 4.4-4.5, 8.2, 8.5, 7.7 | 4P: 35(b), 37, 38 4T: 9 7T: 1, 4, 50 8P: 1, 2(a,b), 19 8T: 2 |
| 6 | Special Discrete Distributions | 4.6-4.8, 7.7 | 4P: 43, 48, 54, 55, 58, 63, 71 4T: 27 4ST: 18 8T: 3(a,b,c) |
| 7 | Continuous RVs: pdf, CDF, Probability, Expectation, MGF; Uniform and Exponential Distributions | 5.1-5.3, 5.5, 7.7 | 5P: 1, 3, 4, 5, 6(b), 7, 10, 13, 32, 34 5T: 12(a,c), 13(a,c), 26 8T: 3(d,e) |
| 8 | Univariate Transformations; Gamma, and Beta Distributions | 5.6-5.7, 7.7 | 5P: 2, 6(a), 8, 37, 39, 41 5T: 14, 18, 25 |
| 9 | Normal Distribution; Joint Distributions: Joint/Marginal PMF and pdf, CDF, MGF; Probability, Expectation, Covariance, Correlation, Independence | 5.4, 6.1-6.2, 7.1-7.2,7.4, 7.7 |
5P: 15, 19, 22 5T: 12(b), 13(b), 30 6P: 1(c), 9(a,b,c,e,f), 15(b,c), 23 7P: 30, 40, 75 7T: 17 |
| 10 | Conditional Distributions, Probability, Expectation; Bivariate Normal | 6.4-6.5,7.5-7.6 | 6P: 40, 42(a) 7P: 50, 51, 65, 72, 77 7T: 40(c), 54, 55 |
| 11 | Multivariate Distributions; Bivariate-to-univariate and Bivariate-to-bivariate Transformations | 6.7 | 6P: 28 , 42(b), 51, 56(b), 57 6T: 33 |
| 12 | Sums of Independent Random Variables, Weak Law of Large Numbers, Central Limit Theorem | 6.3, 7.2, 7.4, 7.7, 8.2, 8.3 | 6P: 33 7P: 6, 31, 39 7T: 12, 48, 51 8P: 5, 7, 14 8ST: 10 |