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MATH 230 - Probability Semester: Spring 2017 Instructors: Lecture hours : Office hours: E-mail : Phone : Deniz Karlı 230.01 Sinan Özeren 230.02 Sinan Özeren 230.03 WWF 236 WWW 123 W5 Room: DMF-203 D/K-209 WWW 678 W5 Room: DMF-203 D/K-209 WW 78 Room: AMF 233 [email protected] [email protected] [email protected] (0216) 528 7190 Teaching Assistant: Lecture Hours: Office Hours: E-mail: Phone: (0216) 528 7180 (0216) 528 7180 Mahmut Kudeyt 230-P.01 : Th 8 230-P.02 : F 4 Room:AMF 238 Th 7 [email protected] (0216) 528 7174 Course Description: Basic Topics in Probability; Probability Axioms, Sample Space, Conditional Probability, Counting Methods. Discrete Random Variables; Probability Mass Function, Families of Discrete Random Variables, Expectations, Function of a Random Variable, Variance and Standard Deviation. Continuous Random Variables; Distribution Function, Probability Density Function, Expected Values, Families of Continuous Random Variables, The normal Distribution. Pairs of Random Variables; Joint Distribution Function, Marginal, Joint Probability Function, Functions of Two Random Variables Course Objectives: The aim of the course is to introduce students to the concepts of probability. Probability is necessary to understand basic modeling and statistical techniques in engineering and in other disciplines. The students learn how to describe quantitatively unpredictable occurrences by using methods and concepts from probability theory. Textbook: Sheldon Ross, A First Course in Probability, Pearson (We’ll use the 9th edition as a reference. But you may use other editions if you already have it. Just double-check the page, chapter and question numbers when homework is assigned since they may vary from edition to edition.) Recommended Readings: 1. Roy D. Yates and David J. Goodman, Probability and Stochastic Processes 2. A Friendly Introduction for Electrical and Computer Engineers, John Wiley, 2005. Week Week of Sections Topics 1.1 Introduction (Read) 1.2 The Basic Principle of Counting; 1.3 Permutations; 1.4 Combinations; 1.5 Multinomial Coefficients 2.1 Introduction 2.2 Sample Space and Events 2.3 Axioms of Probability 2.4 Some Simple Propositions 2.5 Sample Spaces Having Equally Likely Outcomes 3.1 Introduction 3.2 Conditional Probabilities 3.3 Baye’s Formula 3.4 Independent Events 3.5 P(.|F) is a Probability 4.1 Random Variables 4.2 Discrete Random Variables 4.3 Expected Value 4.4 Expectation of a Function of a Random Variable 4.5 Variance 4.6 Bernoulli and Binomial R.V. 4.7 Poisson R.V. 4.8.1 Geometric R.V. --------------- Midterm Exam (April 5) --------------- 1 Feb. 13-17 1.1, 1.2, 1.3, 1.4, 1.5 2 Feb. 20-24 2.1, 2.2, 2.3, 2.4 3 Feb. 27 – March 3 2.4, 2.5 4 March 6-10 3.1, 3.2, 3.3 5 March 13-17 3.4, 3.5 6 March 20-24 4.1, 4.2, 4.3, 7 March 27-31 4.4, 4.5 8 Apr. 3-7 4.6, 4.7, 4.8.1 9 Apr. 10-14 4.9, 4.10 10 Apr. 17-21 5.1, 5.2, 11 Apr. 24-28 5.3, 5.4, 5.5 12 May 1-5 5.7 5.1 Introduction 5.2 Expectation and Variance of Continuous R.V.s 5.3 The uniform R.V. 5.4 Normal R.V.s 5.5 Exponential R.V.s 5.7 Distribution of a Function of a R.V. 6.1 Joint Distribution Functions 13 May 8-12 6.1, 6.2 6.2 Independent R.V.s 14 May 15-18 6.4, 6.5 6.4 Conditional Distributions: Discrete Case 6.5 Conditional Distributions: Continuous Case 4.9 Expected Value of Sums of R.V.s 4.10 Properties of the Cumulative Distribution Function We skip the following sections: 1.6, 2.6, 2.7, 4.8, 5.6, 6.3 Class Policies: Attendance: Attendance to the lectures is highly recommended. Quizzes: There will be 5-10 minutes quizzes every week covering mostly the previous week’s topics. They may be given at anytime during the lectures. So they may be given at the beginning, at the end or in the middle of a lecture. The grades of these quizzes will contribute 55% of your total grade. Notice that without attending weekly quizzes and performing above average, it is quite difficult to pass this course. Homework: There will be assigned sets of questions consisting of problems which target the timely practice of the covered course material but their solutions will not be collected. You are strongly encouraged to work on these questions. Grading: There will be one midterm exam, a final exam and weekly quizzes contributing to the final grade. The PS attendance will be counted toward term grade as well. The weight distributions are as follows: Exams Percent (%) Date Quizzes 55 % Every week, in class Midterm Exam 20 % Wednesday, April 5, @17:00 Final 25 % To be announced later… PS Attendance: Problem sessions are important in understanding the applications of models. Hence it is in your favor to attend them. Exams: Make sure that you take the exams in the correct classroom. Do not forget to bring Işık identification card and an extra official identification card (such as citizen card or driver licence) to the exam. Write exams with pencil only. Dictionaries, calculators and cell phones are not permitted in any exam. There will be a make-up exam (a harder one) only for those students who missed the midterm exam due to a valid excuse. (A doctor’s note is required in case of health issues.) The make-up exam will take place in the last week of classes, will cover all the material included and replace the midterm exam the student has missed. But, questions will be harder than that of the exams given in regular time. In case you miss an exam, you expected to contact with your instructor immediately with a valid document. Supplementary Materials: Some supplementary materials including an archive of recent years exams and lecture notes can be found on the web page: mathport.denizkarli.com/ But note that this web page should not be taken as a replacement for your instructor’s notes. You are responsible on the lecture notes provided by your instructor.