STUDY INFORMATION for Probability (2WS20 2016-2017)

 

Organisation of course:
Lectures and instructions


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


Instructors:
Clara Stegehuis MF 4.091, tel 040-247-7344, c.stegehuis@tue.nl
Lorenzo Federico MF 4.066+067, tel 040-247-8924, l.federico@tue.nl
Alessandro Garavaglia MF 4.066+067, tel 040-247-7310, a.garavaglia@tue.nl

Exam dates:
Final exam: Friday 27-01-2015 09:00-12:00,
Resit: Tuesday 18-04-2015 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.



Studiemateriaal:

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

Statistisch Compendium, dikt.nr. 2218.

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 8.45-10.30 uur in IPO 0.98.
Friday 13.45-15.30 uur in Paviljoen J17.

Instructions:
Tuesday 10.45-12.30 uur in Auditorium 10.
Friday 15:45-17.30 uur in Paviljoen L10.

The lecture and instruction dates are:

15-11, 18-11, 22-11, 25-11, 29-11, 2-12, 6-12, 9-12, 13-12, 16-12, 20-12, 23-12,
10-01-2016, 13-01-2016, 17-01-2016 (exam practice), 20-01-2016 (Final presentations modelling).



Content and approximate division over lectures:

Week 1.1: Sections 1.1 untilt 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 modelling assignment each count for 20% of the final grade.



Modelling Assignment:

The modelling 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. Sometimes, the precise time will be shifted. Carefully inspect the schedule below.

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!).

On the Friday in week 6 a preliminary version of your report needs to be handed in. You will receive comments on this version. It also is part of the grade of your modeling assignment.
You can choose between the following assignments: Modelling assignments. We strive to give each group a unique assignment. During the instructions, you will be told what the procedure for the assignment of assignments is.
Here is the list of groups, their assignments and tutors: Modeling groups, assignments and tutors.



Hand-in exercises:

The last hour of the instruction on Friday afternoon you will make a hand-in exercise maken. Of these 7 hand-in exercise, 3 will be graded. This grade counts for 20% of the final grade.

Exercises for the instructions (these will be updated on a regular basis):

Week 1.1:
C1.2.1, C1.2.5,
C1.3.1, C1.3.4*, C1.3.6*,
C1.4.1, C1.4.2, C1.4.3.


Week 1.2:
C1.4.4, C1.4.6,
C1.5.1, C1.5.4, C1.5.5*, C1.5.9,
C1.7.1*,
C1.8.5, C1.8.11*, C1.8.14.


Week 2.1:
C2.1.2, C2.1.3*, C2.1.4,
C2.3.3* (only first part), C2.3.5,
C2.4.1 (a-c),
C2.5.1, C2.5.4, C2.5.6*,
C2.7.4, C2.7.10.
Fourth hour: Time to ask questions about the modelling assignment.


Week 2.2:
C3.1.1, C3.1.3*,
C3.2.1, C3.2.2(a-c), C3.2.3*, C3.2.5*,
C3.3.1, C3.3.2, C3.3.4*,
C2.7.15*.


Week 3.1:
C3.3.6, C3.3.8*,
C3.4.2*, C3.4.3*,
C3.5.2, C3.5.3.
Extra exercises: C3.4.1*, C3.4.6.


Week 3.2:
C3.5.2, C3.5.3.
C3.6.7*
C3.11.1, C3.11.2, C3.11.4, C3.11.11.
Extra exercises: C3.7.6, C3.7.8*, C3.11.10*.


Week 4.1:
C3.7.1(a)(c)(e), C3.7.7,
C4.1.1(b) [and take f(x)=x^{-2m} for x>1 instead of (c)], C4.1.2, C4.1.3,
Extra exercises: C4.1.1(c).
Fourth hour: Time to ask questions about the modelling assignment.


Week 4.2:
C4.2.1, C4.2.2,
C4.3.1(a), C4.3.3.


Week 5.1:
C4.4.3, C4.4.4, C4.4.5, C4.4.8* (can also be solved directly by estimating the integral),
C4.5.4, C4.5.5, C4.5.7*, C4.5.8.
Extra exercises: C4.3.1(b)(c), C4.3.2*, C4.4.6, C4.5.6*.


Week 5.2:
C4.5.7, C4.5.8*,
C4.6.3, C4.6.4, C4.6.6, C4.6.8,
Extra exercises: C4.6.2, C4.6.5, C4.6.9.


Week 6.1:
C4.7.3, C4.7.13,
C4.8.1, C4.8.3, C4.8.6*,
C4.11.1, C4.11.8,
Extra exercises: C4.7.4, C4.11.10*.
Fourth hour: Time to ask questions about the modelling assignment.


Week 6.2: C4.7.1, C4.7.7*,
C5.10.1, C5.10.2,
exercises on hand-out.
Hand-out Limit Theorems.
Hand in preliminary version of the report for the modelling assigment.


Week 7.1: exercises on hand-out.
Handout Limit Theorems.
Presentation Training.
Instruction: Repeating exercises as well as extra exercises.


Week 7.2: exercises on hand-out.
exercises:

Week 8.1: Practicing exam.

Week 8.2: Final presentations modelling assignments.


Week 9: Exam preparation: Sets of old hand-in exercises.

Hand-in exercises set 1 of 2014 with solutions
Hand-in exercises set 2 of 2014 with solutions
Hand-in exercises set 3 of 2014 with solutions
Hand-in exercises set 1 of 2013 with solutions
Hand-in exercises set 2 of 2013 with solutions
Hand-in exercises set 3 of 2013 with solutions


Vertaling van enkele termen uit de kansrekening en statistiek