printlogo
http://www.ethz.ch/index_EN
Department of Mathematics
 
print
  

Probability and Statistics

Please note that this page is old.
Check in the VVZ for a current information.

Department of Mathematics, ETH Zürich
401-2604, Spring 2016


Lecturer:

Prof. Dr. Halil Mete Soner   HG G 54.3, hmsoner@ethz.ch

Lecture hours:

Tuesday 10:15-12:00 
HG G 5
Friday 8:15-10:00
HG G 5


Beginning from:
Tuesday,  23rd February 2016.

Exercise classes:

Click here to see the exercises.

Yukun He
Wednesday 14:15-16:00
ML F 36
Xinyi Li
Tuesday 13:15-15:00 HG G 26.3
Chong Liu
Tuesday 13:15-15:00 HG E 33.5
Ren Liu
Tuesday 13:15-15:00 HG D 5.2
Yilin Wang (Coordinator)
Tuesday 13:15-15:00 HG D 3.2

Beginning from: Tuesday,  1st March 2016.

Assistants may alternate.

Notes

Content

The main goal is to introduce you to the basic concepts in probability theory and how they are used especially in statistics. Concepts from measure theory course will be mentioned but will not be used in depth in this course. The following topics will be covered, not necessarily in the order listed below. A tentative schedule of all lectures is provided at the end of this page.

  1. Set theoretic aspects;
  2. Uniform distribution;
  3. Conditional probability, Bayes rule;
  4. Independence, correlation;
  5. Random Variables and distributions;
  6. Expected value;
  7. Law of large Numbers;
  8. Central Limit Theorem;
  9. Estimation;
  10. Maximum Likelihood estimator;
  11. Hypothesis testing.

Evaluation

There will be a 3 hour written final examination. More information will be provided towards the end of the semester. Related to this, there will be

Lectures

Version: 20.04.2016 Download

This will be updated during the semester
Please make sure to have the latest version.
DS refers to the book by DeGroot & Schervish,
LN refers to the lecture notes of Föllmer & Künsch.


Lecture Date
-Topic-
1  23.02.2016 Introduction. DS Chapter 1, LN section 2.1
2  26.02.2016 Uniform Distribution. DS Chapter 1, LN section 2.2
3  1.03.2016 Counting, Permutions, etc, DS, Sections 1.7, 1.8.
4  4.03.2016 Conditional Probability.  DS, Chapter 2, LN, section 2.4
5  8.03.2016  Conditional Probability, indepedence.  DS, Chapter 2,  LN, section 2.4
6  11.03.2016 Bernoulli, Poisson.  DS Sections 5.2, 5.4, LN, section 2.6
7  15.03.2016 Non-finite Omega.  LN, section 3.1
8  18.03.2016 Random variables, Distribution, C.D.F. and P.D.F.
DS, Sections 3.1,2, 3, LN, section 3.2
9  22.03.2016 Quantile, Bivariate Distribution, Marginals.
DS, Sections 3.4, 5, LN, section 3.2
    Easter break including the Friday
10  5.04.2016 Independence, Condition Distributions.
DS, Sections 3.6, 7, LN, section 3.2
11  8.04.2016 Expected value, Change of Variables.
DS, Sections 3.8, 4.1, LN, section 3.3
12  12.04.2016 Mean, Variance, Moment Generating Function. DS, Sec-4.3,4,5,6
13  15.04.2016 Conditional Expectation. DS, Sec-4.7. LN, Sec-3.4
14  19.04.2016 Conditional Expectation, Linear Regression. DS, Sec-4.7, Ch-11
15  22.04.2016 Special Distributions. DS, Ch-5.2,3,4,6,7,8
16  26.04.2016 Estimation, prior, posteriori and conjugate distribution.
DS, Sec-7.1, 2, 3. LN, section 6.2
17  29.04.2016 Bayes Estimators. DS, Sec-7.4
18  3.05.2016 Limit Theorems. DS, Chapter 6, LN, chapters 4, 5
19  6.05.2016 Limit Theorems. DS, Chapter 6, LN, chapters 4, 5
20  10.05.2016 Maximum Likelihood. DS, Sec-7.5
21  13.05.2016 Maximum Likelihood. DS, Sec-7.5, 7.6
22  17.05.2016 Sampling distributions. DS, Sec-8.1, 8.2
23  20.05.2016 Sampling distributions. DS, Sec-8.3, 8.4
24  24.05.2016 Confidence Intervals. DS, Sec-8.5
25  27.05.2016 Hypothesis Testing. DS Chapter 8, LN section 6.3
26  31.05.2016 Hypothesis Testing. DS Chapter 8, LN section 6.3
27  3.06.2016 Hypothesis Testing. DS Chapter 8, LN section 6.3

Other questions

Do not hesitate to go and ask

 

Wichtiger Hinweis:
Diese Website wird in älteren Versionen von Netscape ohne graphische Elemente dargestellt. Die Funktionalität der Website ist aber trotzdem gewährleistet. Wenn Sie diese Website regelmässig benutzen, empfehlen wir Ihnen, auf Ihrem Computer einen aktuellen Browser zu installieren. Weitere Informationen finden Sie auf
folgender Seite.

Important Note:
The content in this site is accessible to any browser or Internet device, however, some graphics will display correctly only in the newer versions of Netscape. To get the most out of our site we suggest you upgrade to a newer browser.
More information

© 2016 Mathematics Department | Imprint | Disclaimer | 10 May 2016
top