STUDY INFORMATION for Probability for Mathematics

STUDY INFORMATION for Probability (2WS20 2017-2018)

Organisation of course:
Lectures and instructions

Lecturer:
Prof.dr. Remco van der Hofstad, MF 4.077, tel.040-2472910, rhofstad@win.tue.nl

Instructors:
Souvik Dhara MF 4.091, s.dhara@tue.nl
Youri Raaijmakers MF 4.086, y.raaijmakers@tue.nl
Viktoria Vadon MF 4.072+073, v.vadon@tue.nl

Teaching assistant:
Rowel Gündlach, r.c.gundlach@student.tue.nl

Exam dates:
Final exam: Tuesday 23-01-2018 09:00-12:00,
Resit: Tuesday 17-04-2018 18:00-21:00.

Course material:
Chapters 1 - 4 from Grimmett and Stirzaker, Probability and Random Processes,
except for Sections 1.6, 3.9, 3.10, 4.10, 4.12, 4.13.
In Section 4.7, we only treat the one-dimensional case.
We treat an extended version of Section 5.10, including
the Markov and Chebychev inequalities;
the Weak Law of Large Numbers;
Convergence in distribution;
the Central Limit Theorem.
This part of the course does not follow the book, but rather uses a hand-out.

Books:

Grimmett and Stirzaker, Probability and Random Processes,
Third Edition, Oxford University Press, ISBN 0-19-857222 0.

Statistisch Compendium, dikt.nr. 2218. The compendium can also be used during the exam, so have a look at its useful content.

Prerequisites:

2WBB0 - Calculus variant B (recommended)
2WF40 - Verzamelingenleer en algebra (recommended)
2WA30 - Analyse 1 (recommended)
2WA40 - Analyse 2 (recommended)

Course scheduling:

2 times 2 hours lectures and 2 times 2 hours instructions per week in quartile 2.

Lectures:
Tuesday 13.45-15.30 uur in IPO 0.98.
Thursday 8.45-10.30 uur in IPO 0.98.

Instructions:
Tuesday 15.45-17.30 uur in Dorgelozaal, Traverse.
Thursday 10:45-12.30 uur in Dorgelozaal, Traverse.

Lecture and instruction dates:

14-11, 16-11, 21-11, 23-11, 28-11, 30-11, 05-12, 7-12, 12-12, 14-12, 19-12, 21-12,
09-01, 11-01, 16-01 (exam practice), 18-01 (Final presentations modelling).

Content and approximate division over lectures:

Week 1.1: Sections 1.1 until 1.4 until definition conditional probabilities.

Week 1.2: Sections 1.4, 1.5 en 1.7.

Week 2.1: Chapter 2.

Week 2.2: Sections 3.1-3.3 until definition expectation.

Week 3.1: Sections 3.3-3.6.

Week 3.2: Sections 3.6-3.8.

Week 4.1: Complete Chapter 3. Sections 4.1-4.2.

Week 4.2: Sections 4.2-4.4.

Week 5.1: Sections 4.4-4.6.

Week 5.2: Sections 4.6-4.8.

Week 6.1: Sections 4.9 en 4.11.

Week 6.2: the Markov and Chebychev inequalities, the Weak Law of Large Numbers and proofs;
Formulation of the Central Limit Theorem and examples.

Week 7.1: Proof Central Limit Theorem and further examples.

Week 7.2: Completion course, examples, exercises, practicing CLS.

Week 8.1: Practicing exam.

Week 8.2: Final Presentations Modelling Assignments.

Exam:

There is a written exam that lasts three hours and consists of open questions. During the exam, you can make use of an unwritten Statistisch Compendium and a (grafical) pocket calculator.

In the exam, roughly 50% of the exercises will be more or less standard (as the exercises without star in the instructions), and 50% will require more insight (as the star-exercises in the instructions, or simple proofs). Make sure that you are prepared for both types of questions!

Here are two exams from 2013-2014.
Exam January 24, 2014 with solutions.
Resit exam April 16, 2014 without solutions.

Here is the exam for 2014-2015.
Exam January 23, 2015 with solutions.

Hand-in exercises and the modeling assignment each count for 20% of the final grade.

Modelling Assignment:

The modeling assignment should be chosen in week 1. During the fourth hour on Tuesday morning in weeks 2, 4 and 6 you can ask questions to your supervisors.

You can choose between the following assignments: Modeling assignments. We strive to give each group a unique assignment. Each group is required to send Youri Raaijmakers (y.raaijmakers@tue.nl) a mail with their top 3 preferences for the assignments. The deadline for this is Thursday November 16, 2017. Groups who do not respond will be given an assignment. Once students decide to sign up for the modeling assignment (which happens in week 1 of the course), students are obliged to complete the modeling assignments as a courtesy to their fellow students.

A preliminary version of the report must be handed in Thursday December 21 (Week 6), before 12:00. You will receive feedback on the preliminary report on Tuesday January 9 (Week 7) during the instruction. This preliminary version is also part of the final grade for the modeling assignment. The final report is due on Tuesday January 16 (Week 8) during the instruction. The presentations will be scheduled on Thursday January 18 (Week 8).

We prefer that you write your report in English (note that the assignments are formulated in English as well). Please indicate on your list of preferred assignments whether you write your assignment in English or in Dutch. Those groups that write it in English will receive a bonus of 0.5 grade, and we will be lenient on grammatical and spelling errors in English (contrary to those made in Dutch!). The maximum length of the final report is 15 pages. Groups that write in English also present in English.

Hand-in exercises:

The last hour of the instruction on Thursday mornings you will make a hand-in exercise. These 7 hand-in exercise will all be graded, and you will receive feedback on your solutions as well as on how you write them down. This grade counts for 20% of the final grade. Your 2 worst grades will be dropped. This will also occur when people miss at most 2 hand-in exercises. In the unlikely circumstance that you have to miss more than 2 hand-in exercise, due to good reasons, then let us know beforehand. Then we will strive to find a reasonable solution.

Exercises for the instructions are added regularly, in separate pdf files, with a mix of exercises from the book, extra exercises and questions from old exams.

Week 1.1:
Exercise set Week 1.1.

Week 1.2:
Exercise set Week 1.2.

Week 2.1:
Exercise set Week 2.1.

Fourth hour: Time to ask questions about the modeling assignment.

Week 2.2:
Exercise set Week 2.2.

Week 3.1:
Exercise set Week 3.1.

Week 3.2:
Exercise set Week 3.2.

Week 4.1:
Exercise set Week 4.1.
Fourth hour: Time to ask questions about the modeling assignment.

Week 4.2:
Exercise set Week 4.2.

Week 5.1:
Exercise set Week 5.1.

Week 5.2:
Exercise set Week 5.2.

Week 6.1:
Exercise set Week 6.1.
Fourth hour: Time to ask questions about the modeling assignment.