Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
MATH 131 : Probability Instructor’s Name: Amjad Lone Office No. & Email: 117-A [email protected] Office Hours: TBA TA for the Course: Course Code (Units) Course Description Year: 2002 / 2003 Quarter: Summer Category: TBA Math 131 (4 Units) Basic Probability Theory. Discrete and Continuous Random Variables. Expected Value. Functions of Random Variables. Joint Distributions. Moment Generating Functions. Central Limit theorem and Law of Large Numbers. Core/Elective Core for all Pre-requisites Calculus I Goals 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. Be familiar with central limit theorem and law of large numbers. Math 131 : PROBABILITY Textbooks, Year: 2002 / 2003 Quarter: Summer REQUIRED TEXT Probability and Statistics for Engineers and Scientists by Walpole, R. Myers, and s. Myers, Sixth edition, Prentice Hall International, Inc. Reference Book A first course in Probability by Sheldon Ross 4th edition, Macmillan Publishing Company Lectures, Tutorials & Attendance Policy Grading There will be 25 sessions of 80 minutes each Attendance is not required but strongly recommended since there will be frequent surprise short in-class quizzes. Quizzes Mid-term Exam Final Exam 30% 30% 40% 1 Probability Sample Space Events Counting Sample Points Probability of an Event Conditional probability Multiplicative Rules Bayes’ Rule 4 Ch. 2 2 Random variables and probability distributions Random Variable Discrete Probability Distributions Continuous Probability Distributions Empirical Distributions Double Integration Joint Probability Distribution 4 Ch. 3 3 Mathematical Expectation 5 Ch. 4 Expected Value of a Random Variable Variance and Covariance Mean and Variance Rules Chebyshev’s Theorem Mid-Term Exam 4 5 Discrete Probability Distributions Introduction Discrete Uniform distribution Hypergeometric Distribution Binomial distribution Negative Binomial and Geometric Distribution Poisson Distribution and the Poisson Process 3 Continuous Probability distribution 3 Ch. 5 Ch. 6 Continuous Probability distribution Area Under the Normal Curve Applications of the Normal Distribution Normal approximation to binomial Gamma and exponential distributions 6 Functions of Random Variables Ch. 7 4 Introduction Transformation of Variables Moments and Moment Generating Functions 7 Limit Theorems Sequence of Random Variables The Weak Law of Large Numbers The Central Limit Theorem The Strong Law of Large Numbers 2 Ch. 8 of reference book