COURSE UNIT TITLE

: PROBABILITY THEORY

DEGREE PROGRAMMES

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
MAT 6031 PROBABILITY THEORY ELECTIVE 3 0 0 8

Offered By

Graduate School of Natural and Applied Sciences

Level of Course Unit

Second Cycle Programmes (Master's Degree)

Course Coordinator

Offered to

Mathematics (English)
Mathematics (English)

Course Objective

The course introduces fundamental concepts of measure theory and probability measure
theory. Large sample theory in probability measure spaces is given, including a variety
of convergence results and the central limit theorems.

Learning Outcomes of the Course Unit

1   Understand fundamental ideas of measure theory
2   Demonstrate knowledge of probability laws and conditional probability
3   Set up and solve distributional problems including problems that involve calculus
4   Demonstrate knowledge of properties of well-known probability distributions
5   Calculate the basic two-variable statistics (covariance, correlation) using joint distributions and conditional distributions
6   Obtain the limiting distributions of random variables

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description
1 Basic concepts
2 Special distributions
3 Algebra and transformation of random variables
4 Multivariate normal distribution
5 Families of distributions
6 Set theory and topology
7 Midterm
8 Measure space, Construction of measure space
9 Measurable functions and integration
10 Product of measures Fubini-Tonelli Theorem
11 Derivative of measures Radon-Nikodym Theorem
12 Probability measure, Conditional probability and independence
13 Modes of convergence, Convergence in distribution
14 Limit theorems for summation of independent and non-independent random variables, U-statistics and Martingales

Recomended or Required Reading

1. P. Billingsley: Probability and Measure, J. Wiley, 1995.
2. R. Durrett : Probability: Theory and Examples, Duxbury Press, 1999.

Planned Learning Activities and Teaching Methods

The course consists of lectures, homework and exams

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA
1 MTE 1 MIDTERM EXAM 1
2 MTE 2 MIDTERM EXAM 2
3 FIN FINAL EXAM
4 FCG FINAL COURSE GRADE MTE 1 * 0.30 + MTE 2 * 0.30 + FIN * 0.40
5 RST RESIT
6 FCGR FINAL COURSE GRADE (RESIT) MTE 1 * 0.30 + MTE 2 * 0.30 +RST * 0.40


Further Notes About Assessment Methods

None

Assessment Criteria

To be announced.

Language of Instruction

English

Course Policies and Rules

Attendance to at least 70% for the lectures is an essential requirement of this course and is the responsibility of the student. It is necessary that attendance to the lecture and homework delivery must be on time. Any unethical behavior that occurs either in presentations or in exams will be dealt with as outlined in school policy. You can find the graduate policy at http://web.fbe.deu.edu.tr

Contact Details for the Lecturer(s)

Prof.Dr.SELÇUK DEMIR
e-posta:selcuk.demir@deu.edu.tr
Tel: 0232 301 8581

Office Hours

To be announced.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours)
Lectures 13 3 39
Preparations before/after weekly lectures 13 3 39
Preparation for midterm exam 2 11 22
Preparation for final exam 1 30 30
Preparing assignments 3 12 36
Preparing presentations 1 24 24
Midterm 2 3 6
Final 1 3 3
TOTAL WORKLOAD (hours) 199

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10PO.11
LO.155535435454
LO.25543445554
LO.355534534454
LO.455444534454
LO.555544534444
LO.65543445444

CONTACT INFORMATION
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Phone: +90(232) 412 12 12 - Fax: +90 (232) 464 81 35

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