Huvudsida

Aktuella meddelanden: PAGE UNDER CONSTRUCTION; VLE login page; AUGUST RE-EXAM INFORMATION; The written exam takes place 2012 VIII 29 fm; VLE part of the exam will take place Friday 2012 VIII 31 10 - 12 in rooms ES61 and ES62 I would greatly appreciate if you email me whether you will be taking the re-exam so that we can intervene if the computer rooms would be too small etc.; The rules and setup will be the same as in the January one. Namely :
1) You need to do BOTH the written and VLE part of the examination and on the written part score at least 3 points out of 10.
2) The written part will last two hours and is worth 10points.
3) The VLE part will last two hours and is worth 20points.
4) To pass the exam you need in total to have 40%, see the course webpage for grade table.
5) On the VLE part you may have whatever aids you wish except communicating with others. The VLE part has to be performed at the campus on university computers. On the written exam you will be allowed to have a Chalmers approved calculator and at most one double sided A4 page of own notes.; Unfortunately as it turned out during the January re-exam you will not have access to your VLE part score nor answers. This is completely independent of us and is due to the system being originally designed for another higher education system (the transition to the Swedish system is being worked on). As the re-exam part is to last two hours (it contains more materials than the tests) I have to use the VLE module Exams instead of Tests (the tests can only last one hour). I do not think that it is sensible to setup two separate tests each lasting one hour as this would force you to work on particular questions during a given hour and not allow you to return to them after that hour has passed. Therefore we have decided to use the Exams module so you have the full two hours to work on everything but as a consequence you do not have access to the scores afterwards which we are very sorry about. However after we have went through and graded the exam you are naturally welcome to come and look at the exam through the accounts of the teachers. I understand that this is unfortunate but due to the current implementation of the VLE system we think that this is the most sensible solution.; If you will have any questions about the exam or material please do not hesitate to contact me (preferably by e-mail). I will be available (by email/sometimes in my office) for most of July but then will be on vacation 30 July to 20 August (or longer) with practically no email access. If you will have questions then please contact the exercise teachers.; JANUARAY RE-EXAM INFORMATION; Concerning the re-exam there are a couple of points to remember :; 1) The written re-exam is : 11 January 2012 at 14:00.; 2) There will be two types of the re-exam. One for current year students (worth 10points, result will sum with the VLE re-exam and lasting till 16:00) and another for students of previous years (worth 30points, like the exams in previous years and lasting till 16). Unless anything will change, at the examination you just say which paper you take. However you may NOT take both, look at them and then decide which one you prefer and this option of re-exam choice is only open to students from previous years NOT to current year students.; 3) If you take the new re-exam then to pass you also HAVE to take the VLE part of the re-exam. This will take place on January 16 2012, 8 - 10 in ES61.; 4) As ES61 has only 17 computers, it was chosen as this is more than the number of people who failed the ordinary exam. However I am aware that some people might want to raise their grade (in which case you HAVE to also do BOTH parts of the re-examination) or just did not show up on the ordinary exam. Therefore please drop me an email if you intend to (for whatever reason) do the new VLE type re-exam so in case there are more people I will be able to book another computer room.; If you have any questions please contact me (via e-mail).; The lectures will be given in English, exercise classes in Swedish.; A short statistical English, Swedish dictionary is here; See also the previous years course web page for more information (in Swedish)

Schedule: Monday 2011 VIII 29 Introductory lecture 11:00-11:45 in HB3; Monday 2011 X 10 Exercise session 15:15-17:00 in ES51, ES52, ES53

Examinator och föreläsare: Lecture; Krzysztof Bartoszek [krzbar _[ at ]_ chalmers _dot_ se]; Exercises; Fredrik Boulund [fredrik.boulund _[ at ]_ chalmers _dot_ se]; Roza Maghsood [ rozam _[ at ]_ chalmers _dot_ se ]; Viktor Jonsson [ v.a.jonsson _[ at ]_ gmail _dot_ com ]

Kurslitteratur: (A) J. Anderson, J. Bell, J. Anderson Discrete Mathematics with Combinatorics (will be used only for one exercise session); (EG) K. Eriksson, H. Gavel Diskret matematik Studentlitteratur (will be used only for one exercise session); (GS) C. Grinstead, J Snell Introduction to Probability AMS ( Available online ); (MA) J. Milton, J. Arnold Introduction to Probability and Statistics McGraw-Hill (Course textbook); VLE textbook (auxillary material for computer labs); An online textbook in Swedish on Markov Chains can be found in pdf here.

Preliminary lecture plan

Dag	Avsnitt	Innehåll
2011 VIII 30		Introduction to the course
2011 VIII 30	(MA) Ch 1, 2	Basic definitions and probability laws
2011 IX 01	(MA) Ch 3.1 - 3.5	Discrete random variables
2011 IX 06	(MA) Ch 4.1, 4.2, 4.4 - 4.6	Continuous random variables
2011 IX 08	(MA) Ch 5.1 - 5.3	Joint distributions (multivariate random variables)
2011 IX 13	(GS) Ch 11.1	Introduction to Markov Chains
2011 IX 15	(MA) Ch 3.8, 4.3	Introduction to Poisson processes
2011 IX 20	(MA) Ch 6.1, 6.3, 7.1, Theorem 7.3.4, 7.4, 8.1, 8.2	Estimation and Confidence Intervals, Central Limit Theorem
2011 IX 22	(MA) Ch 6.1, 6.3, 7.1, Theorem 7.3.4, 7.4, 8.1, 8.2	Confidence intervals (continued), introduction to statistical tests
2011 IX 27	(MA) Ch 9.1, 9.3	Inferences on proportions
2011 IX 29	(MA) Ch 9.3, 10.1, 10.3	Confidence intervals for proportions
2011 X 04	hand outs	Generating functions, Merge sort time complexity
2011 X 06	(MA) Ch 3.4 (mgf sec.), 7.3 (GS) Ch 8	Moment generating functions, law of large numbers
2011 X 11	(MA) 11.1, 11.2, 11.3	Linear regression
2011 X 13	(MA) 10.6	(?)Introduction to non-parameteric tests, introduction to Bayesian statistics, revision

Exercise classes

The majority of exercise sessions will take place in computer labs (depending on day ES61, ES62, ES63, ED2480, HC105) however there will be some blackboard exercise sessions (in rooms ES51, ES52, ES53 on days 20 IX, 4 X, 6 X and 10 X). The computer labs will be based on Mathematical Sciences department's Stats VLE which is a web-based system providing students with necessary tools to learn basic Probability and Statistics and practice problem solving on your own. It contains a variety of computer generated questions covering the course curriculum as well as all necessary supporting materials: statistical tables, demos, etc. One may re-run the question-solution cycle as many times as felt necessary to deepen understanding of Statistics and to practice the techniques. It is complemented by the Study Guide with necessary theory which is directly accessible from within the VLE. Instructions on how to get started are given at the first lecture.

2011 IX 20	7.47, 7.48, 7.49, 7.53, 7.55, 7.56, 8.23, 8.24
2011 X 04	(EG) 6.18bc (A) 13.2.1, 13.2.3, 13.3.11, 13.3.23, 13.3.37
2011 X 06	(MA) 3.32, 3.34 (GS) 8.1.4, 8.1.8, 8.2.1, 8.2.2, 8.2.10
2011 X 10	Question and answer session, project consultation

Recommended exercises for self study (at home)

Solutions to some of the exercises from the textbook

Week	Exercises
I	(MA) 1.3, 1.5, 1.7, 1.8, 1.10, 1.16, 1.27, 1.36, 1.37, 2.2, 2.3, 2.4, 2.6, 2.9, 2.11, 2.14, 2.15, 2.16, 2.19, 2.20, 2.23, 2.24, 2.34, 2.36, 2.40, 2.41, 3.7, 3.8, 3.9, 3.10, 3.19, 3.20 (and Var[x]=E[x^2]-(E[x])^2), 3.21, 3.24abe, 3.31abeg, 3.40, 3.41, 3.42 ,
II	(MA) 3.7, 3.8, 3.9, 3.14, 3.25abe, 3.31abeg, 3.38, 3.40, 3.42, 3.79, 4.1, 4.4, 4.5, 4.6, 4.9, 4.10, 4.13, 4.16, 4.18, 4.19, 4.39, 4.41, 4.42, 4.44, 4.70, 4.71, 4.75, 4.77, 5.1, 5.5, 5.4, 5.15, 5.16, 5.24, 5.25, 5.26, 5.29, 5.35, 5.37
III	(GS) 11.1.2, 11.1.3, 11.1.5, 11.17, 11.1.11, 11.2.1, 11.2.3, 11.2.19a (MA) 5.1, 5.4, 5.16, 5.35, 3.61, 3.62, 3.64, 3.70, 4.34, 4.35, 4.36, 4.37, 7.3, 7.5
IV	(MA) 3.64, 3.68, 3.70, 4.36, 4.37, 7.1, 7.4, 7.6, 7.10, 7.12, 7.18, 7.45, 7.50, 7.53, 6.1, 6.3, 6.24bce, 6.34abc, 8.2, 8.5, 8.9, 8.11, 8.17
V	(MA) 4.52, 4.53, 4.54, 4.55, 8.1, 8.2, 8.4, 8.5, 8.9, 8.10, 8.11, 8.13, 8.17, 9.1, 9.2, 9.6, 9.17, 9.18, 9.19, 9.20, 10.2, 10.4, 10.18, 10.19 (assume equal variance and skip a)
VI	(EG) 6.18ad, 6.19abc, 6.20 (A) 13.2.7, 13.2.9, 13.3.13, 13.3.35, 13.2.21 (MA) 3.31, 3.35, 7.38, 7.45
VII	(MA) 3.31, 3.35, 7.38, 7.45, 11.1a, 11.28, 11.29 (CIs), Fig 11.20, 11.33, 11.34, 11.62, 11.63, 11.65, 11.66, 10.1 (non parametric test), 10.10(non parametric test) (GS) 8.1.1, 8.1.11, 8.2.5, 8.2.9

Home assigments: There will be three home assignments to be handed-in. You have to hand in all three hand-ins to pass the course. They can be done either individually or in groups of up to four. For each assignment you have to hand in a report. If the assignment is done in a group then evey member of the group has to have contributed to each part of the assignment and understand everything in it. I reserve the right to ask students to explain their work if I feel it will be necessary.; Assignment 1 Due data 2011 IX 12 (will be posted 2011 VIII 29); Handle returns with exercise teachers; Assignment 2 Due data 2011 IX 26 (will be posted 2011 IX 12); Handle returns with exercise teachers; Assignment 3 Due data 2011 X 10 (will be posted 2011 IX 26); Handle returns with exercise teachers; The graded assigments will be brought to the first lecture after grading and afterwards can be picked up (along with all the returns) in the box outside my office, L3098 in the Maths building. All returns must be handled with the exercise session teachers.

Kurskrav: The course is an introduction to probability theory and statistics with elements of discrete mathematics for non-mathematical students. It will put emphasis on the practial usage of statistics but within a rigorous framework. After passing the examination the student should be familiar with fundamental statistical and probabilistic concepts. The student should be able to perform estimatiion of the mean, variance, work with proportions and confidence intervals. The course also familiarizes the student with the Central Limit Theorem, the Law of Large Numbers and fundamental probabilistic inequalities. The student after the should also be familiar with the techniques of generating functions and moment generating functions. The course will teach how to do basic analysis of data and state the problem and results in a statistical language.

Examination

The grade for the examination consists of two parts, the hand-ins and exam. To pass the course one has to hand-in all three hand-ins and pass the exam. The exam consists of three parts, two VLE tests 15 September and 13 October and a final exam concerning mostly theory and sections not covered by VLE. Each of the tests and exam consists of 10 points. To pass one has to score at least 40% in total from the above and ALSO get at least 3 points on the final exam. Take note that the first VLE test is very EARLY on in the term. The final grade will be as follows,

Grade	Points	Percentage
3	[12 - 18)	[40% - 60%)
4	[18 - 24)	[60% - 80%)
5	[24 - 30]	[80% - 100%]

Tentamina: On the VLE tests you may have whatever aids you wish except communicating with others. The tests have to be performed at the campus on university computers. On the final exam you will be allowed to have a Chalmers approved calculater and at most one double sided A4 page of own notes.
: Meddelande om resultat fås enbart med epost via LADOK. (Ej muntligt på studieexpeditionen.) Detta sker automatiskt när resultaten är registrerde.
Kontrollera att Du har fått rätt betyg och att poängsumman stämmer.
Vid ordinarietentamen:: Ett granskningstillfälle av tentamen är obligatoriskt. När detta äger rum meddelas på kurshemsidan. Den som inte kan delta vid granskningen kan sedan hämta och granska sin tenta Matematiska vetenskapers studieexpedition, måndag till fredag, kl 8.30-13.00. Eventuella klagomål på rättningen ska lämnas skriftligt (på expeditionen finns en blankett till hjälp).
: Vid omtentamen:
Tentorna granskas och hämtas ut på Matematiska vetenskapers studieexpedition, måndag till fredag, kl 8.30-13.00. Eventuella klagomål på rättningen ska lämnas skriftligt (på expeditionen finns en blankett till hjälp).; Följande länk berättar mer om reglerna kring att tentera på Chalmers: att tentera

Gamla Tentor

2012 I 11 New style	English Swedish	Solutions
2012 I 11 Old style	English Swedish	Solutions
2011 X 18	English Swedish	Solutions
2011 VIII 23	English Swedish	Solutions
2011 I 12	English Swedish	Solutions
2010 IX 19	English Swedish	Solutions
2010 VIII 24	Exam	Solutions
2010 I 13	Exam	Solutions
2009 X 19	Exam	Solutions
2009 VII 25	Exam	Solutions
2009 I 14	Exam	Solutions
2008 X 21	Exam	Solutions
2008 VIII 26	Exam	Solutions
2008 I 16	Exam	Solutions
2007 X 23	Exam	Solutions
2007 VIII 28	Exam	Solutions
2007 IV 10	Exam	Solutions
2006 XII 21	Exam	Solutions
2006 I 11	Exam	Solutions (Skip 5)
2005 XII 16	Exam	Solutions
2005 X 18	Exam	Solutions (Skip 5 och 6)
2004 VIII 24	Exam	Solutions (Skip 7)
2004 XII 18	Exam	Solutions

Day	Time	Place	Remark
Monday	13:15-15:00	HB3	Lecture
Tuesday	10:00-11:45	See eg Timeedit depends on day	Exercises
Wednesday	10:00-11:45	HC1	Lecture
Thursday	10:00-11:45	See eg Timeedit depends on day	Exercises

2011 X 18 fm	Ordinary exam date
2012 I 11 em	Re-examination
2012 VIII 29 fm	Re-examination