Syllabus

Title
2091 Probability and Statistics (Science Track)
Instructors
Assoz.Prof. PD Dr. Zehra Eksi-Altay, BSc.MSc.
Contact details
  • Type
    PI
  • Weekly hours
    2
  • Language of instruction
    Englisch
Registration
11/20/19 to 11/29/19
Registration via LPIS
Notes to the course
Subject(s) Master Programs
Dates
Day Date Time Room
Monday 12/02/19 03:30 PM - 05:30 PM D4.0.022
Thursday 12/05/19 03:00 PM - 05:00 PM D3.0.225
Monday 12/09/19 03:30 PM - 05:30 PM D4.0.022
Thursday 12/12/19 03:00 PM - 05:00 PM TC.3.21
Monday 12/16/19 03:30 PM - 05:30 PM D4.0.022
Thursday 12/19/19 03:00 PM - 05:00 PM TC.3.21
Monday 01/13/20 03:30 PM - 05:30 PM D4.0.022
Thursday 01/16/20 03:00 PM - 06:00 PM TC.3.21
Monday 01/20/20 03:30 PM - 06:30 PM D4.0.022
Thursday 01/23/20 03:00 PM - 05:00 PM D4.0.022
Friday 01/24/20 04:00 PM - 06:00 PM D3.0.225

Contents

This course is a graduate course intended for Economics Masters students. The course aims at building theoretical statistics starting from the basics of probability theory. In particular, the purpose of this course is to give further knowledge in statistics and probability theory which is essential for econometrics and statistical modeling.

Learning outcomes

After completing this class successfully the student will have the ability to:

  • define, describe and work with the basic concepts in probability and statistics,
  • use methods and ideas from probability and statistics to solve scientific problems,
  • solve practical problems and interpret the results.


Attendance requirements

Attendance of at least 80% of the classes is necessary to fulfill the requirements.

Teaching/learning method(s)

The course consists of lectures, accompanying homework assignments and one midterm and the final examinations. The lecture part presents the theoretical concepts. There will be 4 homework assignments related to the subjects covered during the lecture. Students are allowed to hand in the assignments as a group of at most three people.

Assessment

  • 20 % Homework assignments
  • 30 % Midterm Exam
  • 50 % Final Exam


Prerequisites for participation and waiting lists

Familiarity with mathematical concepts such as basic set theory, convergence of sequences and functions, continuity, linear maps and matrices, definite and indefinite integral, differentiation, and Taylor polynomial series is expected. Knowledge in basic probability theory and statistics is desirable.

Readings

1 Author: [CB] Georg Casella and Roger l. Berger
Title: Statistical Inference

Publisher: Duxbury Press
Edition: 2nd
Year: 2001
Type: Book
2 Author: Ramu Ramanathan
Title: Statistical Methods in Econometrics

Publisher: Academic Press
Remarks: abbreviated RR
Year: 1993
3 Author: M. R. Spiegel, J. J. Schiller, R. A. Srinivasan
Title: Schaum’s Outlines of Probability and Statistics

Publisher: McGraw-Hill
Edition: 3rd ed. ISBN 978-0-07-154425-2
Remarks: Chapter 1-4
Year: 2009
4 Author: J. A. Rice
Title: Mathematical Statistics and Data Analysis

Publisher: Wadsworth&Brooks/Cole ISBN 0-534-08247-5
Remarks: Chapter 1-5
Year: 1988

Availability of lecturer(s)

zehra.eksi@wu.ac.at

Unit details

Unit Date Contents
1

Basics of probability, conditional probability and independence, random variables, distribution functions.

Reference: CB chapter 1, 2.


2

Transformations of random variables, expected values, moments and moment generating functions.

Reference: CB chapter 2,3.


3

Discrete distributions, continuous distributions.

Reference: CB chapter 3.


4

Multivariate distributions, joint and marginal distributions. 

Reference: CB chapter 4.


5

Multivariate normal, Chi-square distribution, multinomial distribution, probability inequalities.

Reference: CB chapter 4.

6

Midterm Exam


7

Sampling theory, random samples, sampling distributions, convergence concepts, law of large numbers, central limit theorem.

Reference: CB chapter 5


8

Estimation: Methods of finding estimators; maximum likelihood estimators, method of moments, Bayes estimators.

Reference: CB chapter 7.

9

Estimation: Methods of evaluating estimators; mean squared error, best unbiased estimators, sufficiency and unbiasedness.

Reference: CB chapter 7.

10

Basic concepts of hypothesis testing, methods of finding tests (Likelihood ratio test, etc.)

Reference: CB Chapter 8 

11

Hypothesis testing; methods of evaluating tests.

Reference: CB chapter 8.


12 Final Exam
Last edited: 2019-03-20



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