COURSE UNIT TITLE

: PROBABILITY AND STATISTICAL INFERENCE - I

DEGREE PROGRAMMES

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
STA 5053 PROBABILITY AND STATISTICAL INFERENCE - I COMPULSORY 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 ÖZLEM EGE ORUÇ

Offered to

Statistics
STATISTICS
Statistics

Course Objective

This course is a rigorous introduction to the mathematical theory of probability, and it provides the necessary background for the study of mathematical statistics and probability modeling.

Learning Outcomes of the Course Unit

1   An understanding of fundamental ideas of probability 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 distributions of the functions of random variables
7   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 Set theory , the probability set function, probability space
2 Some properties of probability, conditional probability and independence
3 Random variables of the discrete type, random variables of the continuous type
4 Properties of the distribution function
5 Expectation of random variable, some special expectation, Chebyshev's Inequality
6 Some Special Discrete Distributions, Preparing Individual Assignments
7 Some Special Continuous Distributions
8 Mid-term
9 Distributions of two Random Variables
10 Conditional Distributions and Expectations
11 Covariance , Correlation coefficient and independent random variables
12 Methods for distributions of functions of random variables (CDF and Transformation Methods)
13 Distribution of sums of random variables (MGF technique and Convolution), Order Statistics
14 Limiting Distributions

Recomended or Required Reading

Textbook(s):
1)R. V. Hogg and A.T.Craig, Introduction to Mathematical Statistics, 5th Edition, Prentice Hall.
2) R. J. Larsen and M. L. Marx, An Introduction to Mathematical statistics and Its Applications, 4th Edition, Prentice Hall.

Supplementary Book(s):

1. William Feller, An introduction to probability theory and its applications
2. Dimitri P. Bertsekas , John N. Tsitsiklis, Introduction to Probability 1st Edition
3.L. J. Bain and M. Engelhardt, Introduction to Probability and Mathematical Statistics, 2nd Edition, Duxbury, 1992.

Planned Learning Activities and Teaching Methods

The course consists of lecture, problem solving and homework.

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA
1 MTE MIDTERM EXAM
2 ASG 1 ASSIGNMENT 1
3 ASG 2 ASSIGNMENT 2
4 FIN FINAL EXAM
5 FCG FINAL COURSE GRADE MTE * 0.25 + ASG1 +ASG 2/2 * 0.25 + FIN * 0.50
6 RST RESIT
7 FCGR FINAL COURSE GRADE (RESIT) MTE * 0.25 + ASG 1 +ASG2/2 * 0.25 + RST * 0.50


*** Resit Exam is Not Administered in Institutions Where Resit is not Applicable.

Further Notes About Assessment Methods

None

Assessment Criteria

Evaluation of exams and homework.

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)

DEU Faculty of Sciences Department of Statistics
Prof.Dr. Özlem EGE ORUÇ
e-posta:ozlem.ege@deu.edu.tr
Tel: 0232 301 85 58

Office Hours

To be announced.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours)
Lectures 14 3 42
Preparations before/after weekly lectures 14 1 14
Preparation for midterm exam 1 30 30
Preparation for final exam 1 40 40
Preparing assignments 2 20 40
Final 1 2 2
Midterm 1 2 2
Project Assignment 2 10 20
TOTAL WORKLOAD (hours) 190

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10
LO.154
LO.254
LO.354554
LO.45554
LO.55554
LO.65554
LO.7554

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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