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.
Syllabus

Type
PI 
Weekly hours
2 
Language of instruction
Englisch
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 
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 of at least 80% of the classes is necessary to fulfill the requirements.
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.
 20 % Homework assignments
 30 % Midterm Exam
 50 % Final Exam
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.
zehra.eksi@wu.ac.at
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, Chisquare 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 
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