Download Syllabus-Math230

MATH 230 - Probability
Semester: Summer ‘17
Deniz Karlı
Instructor:
Lecture hours :
Office hours:
WWW WWW 123 678
Room: AMF 233
TW 55
E-mail :
[email protected]
Phone :
(0216) 528 7190
Teaching
Assistant:
Lecture
Hours:
Office Hours:
E-mail:
Phone:
Mahmut Kudeyt
ThTh 12
ThTh 56 / AMF 238
[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, Variance, Covariance and Correlation Concepts, Moment
Generating Function, Central Limit Theorem
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: Roy D. Yates and David J. Goodman, Probability and
Stochastic Processes
A Friendly Introduction for Electrical and Computer Engineers, John Wiley, 2005.
Week
1
2
3
4
Week of
July 5
July 12
July 19
July 26
Sections
Topics
1.1, 1.2, 1.3,
1.4, 1.5, 2.1,
2.2, 2.3, 2.4
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, 2.5, 3.1,
3.2, 3.3
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 & ODDS Notation
3.4, 3.5, 4.1,
4.2, 4.3, 4.4
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
4.5,4.6, 4.7,
4.8.1
4.5 Variance
4.6 Bernoulli and Binomial R.V.
4.7 Poisson R.V.
4.8.1 Geometric R.V.
------- Exam 1 (July 26 @ 14:00 in our classroom) -----------
5
Aug 2
4.9, 4.10, 5.1,
5.2, 5.3, 5.4
4.9 Expected Value of Sums of R.V.s
4.10 Properties of the Cumulative Distribution Function
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
Aug. 9
5.5, 5.7 ,
------ Exam 2 (Aug 9 @ 14:00 in our classroom) ----------
7
Aug. 16
6.1, 6.2, 6.3,
6.4, 6.5
6.1 Joint Distribution Functions
6.2 Independent R.V.s
6.3 Sums of Independent R.V.s
6.4 Conditional Distributions: Discrete Case
6.5 Conditional Distributions: Continuous Case
We skip the following sections: 1.6, 2.6, 2.7, 4.8, 5.6
(*) These sections will be covered if time permits. Your Instructor will inform you
about these section at the end of the term.
Class Policies:
Attendance: Attendance to the lectures is highly recommended. It will be graded toward
5% of the term grade. Attendance will be taken both in the mornings and in the
afternoons.
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 two exams, a final exam and attendance contributing to the term
grade. The weight distributions are as follows:
Exams
Percent (%)
Date
Attandence
5%
Exam I
30 %
July 26 @ 14:00
Exam II
30 %
August 9 @ 14:00
Final
35 %
To be announced later…
Exams: They will be held in our classroom. Do not forget to bring Işık identification
card 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 ONE of
the midterm exam due to a valid excuse. If you missed both midterms, the makeup will
be counted toward only one of the exams, and the other missed exam will be counted as
zero. 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 much 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.
Useful Source: you can find some course related material on the web page
mathport.denizkarli.com . There are some useful links, previous year’s exams and
solutions and some lecture notes. They are free. You can print and use them by respecting
copyrights.