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MATH 203 – Introduction to Probability Instructor: Firdevs Ulus Email: [email protected] Office: TBA Office hours: TBA Textbook: John Freund’s Mathematical Statistics with Applications, 8th Edition, Pearson-Prentice Hall Supplementary Text: S. Ross: A First Course in Probability, 7th Edition, PearsonPrentice Hall Grading: Midterms each 30%, Final Exam 40% Midterm I: Saturday, July 20, 10:00-12:30 Midterm II: Saturday, August 3, 10:00-12:30 Final date will be announced later. You will be given ONLY one make-up exam for the midterms so you cannot get make-up exam for both of the midterms. If you miss the final, you need to notify the instructor (preferably via email) within 48 hours after the exam. A make-up exam will be offered ONLY IF the student provides a valid excuse endorsed by substantial evidence like hospital or the University Health Center reports. It is strongly recommended that you do NOT miss the Final exam. The makeup exam tends to be much more difficult. If you miss two or more exams your grade will be NA, and you will NOT be able to take the retake exam. Important: No attendance will be taken during lectures. However, if you come to the lectures, you MUST respect the instructor and your classmates. Under no circumstances, you can distract your friends (text-messaging, chatting, etc.). TENTATIVE SCHEDULE Chapter 1: Introduction and Combinatorial Methods The Basic Principles of Counting Permutations Combinations Multinomial Coefficients Chapter 2: Probability Sample Space and Events Postulates of Probability Some Rules of Probability Conditional Probability Independent Events Bayes’ Theorem Chapter 3: Probability Distributions and Densities Random Variables Discrete Probability Functions and Cumulative Distribution Functions Continuous Probability Densities and Cumulative Distribution Functions Multivariate Distributions Marginal and Conditional Distributions Chapter 4: Mathematical Expectation The Expected Value of a Random Variable Moments, Variance Chebyshev’s Theorem Moment Generating Functions Product Moments, Covariance Moments of Linear Combinations of Random Variables Conditional Expectations Chapter 5: Special (Discrete) Probability Distributions The Uniform Distribution The Bernouilli and Binomial Distributions The Negative Binomial and Geometric Distributions The Hypergeometric Distribution The Poisson Distribution The Multinominal Distribution Chapter 6: Special Probability Densities (Selected Sections) The Uniform Distribution The Gamma, Exponential and Chi-Square Distributions The Normal Distribution The Normal Approximation to the Binomial Distribution Chapter 7: Functions of Random Variables (Selected Sections) Distribution Function Technique Transformation Technique: One Variable Moment Generating Function Technique Chapter 8: Sampling Distributions (Selected Sections) Samples, the Distribution of the Mean The Law of Large Numbers, the Central Limit Theorem Note: Lecture note will be posted on SUCourse.