Download Syllabus-Math230

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.