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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.