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MATH 131 : Probability Zartash Afzal Uzmi Instructor’s Name: Office No. & Email: 2129 [email protected] Office Hours: TW 4pm-5pm Course Description Quarter: Autumn Category: Math 131 (4 Units) Basic Probability Theory. Discrete and Continuous Random Variables. Functions of Random Variables. Expectations. Joint Distributions. Moment generating functions. Core/Elective Core for all Pre-requisites Calculus I Goals 2002 / 2003 Nooruddin Abbas Ali Shah TA for the Course: Course Code (Units) Year: To acquire a mathematical understanding of Probability Theory. Be familiar with discrete (e.g., Bernoulli and Binomial) and continuous (e.g., Uniform and Normal) Probability distributions. Be able to compute densities and expectations of transformations and sums of random variables. To understand the concept of sampling distributions. Math 131 : PROBABILITY TextBooks, Programming Environment, etc. Year: 2002 / 2003 Quarter: Autumn REQUIRED TEXT: A first course in Probability by Sheldon Ross Other References: Modern Elementary Statistics by John E. Freund. Prentice / Hall International editions. Lectures, Tutorials & Attendance Policy There will be 30 sessions – 20 of 75 minutes each 10 of 50 minutes each Attendance is not required but strongly recommended since there will be frequent surprise short in-class quizzes. Grading Homeworks Quizzes Mid-term Exam Final Exam 10% 20% 30% 40% Regrading Deadlines (after graded item returned) Homeworks Quizzes Mid-term Exam Final Exam (No exceptions) 2days 2days 5days End of first week of winter quarter Math 131 : PROBABILITY Module 1 2 Topics Permutations and Combinations Multinomial Coefficients Year: 2002 / 2003 Quarter: Autumn Sessions Readings 6 Ch. 1 Events Sample Space Counting Sample Points Probability of an Event Axioms of Probability Ch. 2 Conditional Probability Independence Bayes’ Rule Ch. 3 Random Variables Distribution Functions (cdf, pdf) Discrete Random Variables Expected Value of Discrete Random Variables Variance Examples of Discrete Random Variables 7 Ch. 4 Continuous Random Variables Expectation and Variance Uniform Random Variable Normal Random Variable Exponential Random Variable Distribution of a Function of Random Variable 5 Ch. 5 Joint Distributions Conditional Distributions Order Statistics 4 Ch. 6 4 Covariance and Correlation Conditional Expectation Moment Generating Functions 4 Ch. 7 5 Limit Theorems Markov Inequality Chebyshev's Inequality The Central Limit Theorem 3 Ch. 8 Mid-Term Examination 3