COURSE UNIT TITLE

: ADVANCED PROBABILITY THEORY

DEGREE PROGRAMMES

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
STA 6003 ADVANCED 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

PROFESSOR DOCTOR TUĞBA YILDIZ

Offered to

Statistics (English)
STATISTICS (ENGLISH)
Statistics (English)

Course Objective

This course aims to make the students familiar with the advance concepts of probability theory, its applications and statistics.

Learning Outcomes of the Course Unit

1   Find probabilities of events
2   Work with discrete distributions, being able to compute important characteristics for them
3   Work with continuous distributions and find basic characteristics for them
4   Analyze bivariate distributions, compute various characteristics for them
5   Derive the law, strong law of large numbers and the central limit theorem for the sums of independent random variables

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description
1 Probability Measure on a Sigma-Algebra and its Properties
2 Conditional probability and independence
3 Random variables and their properties
4 Bivariate random variables and their distribution functions
5 Conditional Distributions, Independent Random Variables
6 Properties of Expectation
7 Conditional Expectation
8 Martingales
9 Moment Generating Functions
10 Characteristic function
11 Distribution of sums of random variables
12 On convergence of random variables and distributions
13 Limit theorems
14 The central limit theorem and the law of large numbers

Recomended or Required Reading

Textbook(s):
P. Billingsley, Probability and Measure, J. Wiley, 1995.
R. Durrett, Probability: Theory and Examples, Duxbury Press, 1999.
Ash R.B. Basic Probability Theory, John Wiley & Sons Inc; First Edition edition (1970).
W. Feller An introduction to probability theory and its applications, Vol. I, Wiley, 1968.
W. Feller An introduction to probability theory and its applications, Vol. II, Wiley, 1971.

Planned Learning Activities and Teaching Methods

The course consists of lecture, homework.

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA
1 MTE MIDTERM EXAM
2 ASG ASSIGNMENT
3 FIN FINAL EXAM
4 FCG FINAL COURSE GRADE MTE * 0.40 +ASG * 0.10 +FIN * 0.50
5 RST RESIT
6 FCGR FINAL COURSE GRADE (RESIT) MTE * 0.40 +ASG * 0.10 +RST * 0.50


Further Notes About Assessment Methods

None

Assessment Criteria

Evaluation of exams and homeworks.

Language of Instruction

English

Course Policies and Rules

Attendance is an essential requirement of this course and is the responsibility of the student. Any unethical behavior that occurs either in presentations or in exams will be dealt with as outlined in school policy. You can find the undergraduate policy at www.fef.deu.edu.tr.

Contact Details for the Lecturer(s)

DEU. Faculty Sciences Department of Statistics B003
e-mail: selma.erdogan@deu.edu.tr
Tel: 0232 301 85 71

Office Hours

To be announced.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours)
Lectures 14 3 42
Preparing assignments 2 15 30
Preparations before/after weekly lectures 14 1 14
Preparation for final exam 1 45 45
Preparation for midterm exam 1 55 55
Final 1 2 2
Midterm 1 2 2
TOTAL WORKLOAD (hours) 190

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10
LO.154223
LO.254223
LO.354223
LO.454223
LO.554223

CONTACT INFORMATION
Dokuz Eylül Üniversitesi Cumhuriyet Bulvarı No: 144 35210 Alsancak / İZMİR
Phone: +90(232) 412 12 12 - Fax: +90 (232) 464 81 35

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