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Welcome to the course.
The lectures will be given in English, exercise classes in English and Swedish.
The schedule for the course can be found via the Course Schedule link on top of the page.
You may use this map to find the location of the various rooms.
Teachers
Lecturer: Alexey Lindo
Teaching Assistant: Marco Longfils, Roza Maghsood
Student representatives
Course reps: Isak Persson, Andre Perzon, Robert Slipac, Jacob Spilg and Jonas Åkesson
Course literature
(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) VLE textbook (auxillary material for computer labs)
An online textbook in Swedish on Markov Chains can be found in pdf here.
Syllabus
The full schedule is available here.

Lectures and exercise sessions
p
Week/Day Lecture/Exercise session
Preliminary Contents
w36(1)


Mon. 31 Aug.

13:15 - 16:00

Lecture

Room HC2

Introduction to the course

Basic definitions and probability laws

(MA) Chapters 1, 2

Tue. 1 Sep.

10:00 - 11:45

Exercise session

Rooms ES61, ES62, ES63

VLE

Wed. 2 Sep.

10:00 - 11:45

Lecture

Room HC2

Discrete random variables

(MA) Chapters 3.1 - 3.5

Thu. 3 Sep.

10:00 - 11:45

Exercise session

Rooms ES61, ES62, ES63

VLE

w37(2)


Mon. 7 Sep.

13:15 - 15:00

Lecture

Room HC2

Continuous random variables

(MA) Chapters 4.1, 4.2, 4.4 - 4.6

Tue. 8 Sep.

10:00 - 11:45

Exercise session

Rooms ES61, ES62, ES63

VLE

Wed. 9 Sep.

10:00 - 11:45

Lecture

Room HC2

Joint probability distributions

(MA) Chapters 5.1 - 5.3

Thu. 10 Sep.

10:00 - 11:45

Exercise session

Rooms ES61, ES62, ES63

VLE

w38(3)


Mon. 14 Sep.

13:15 - 15:00

Lecture

Room HC2

Introduction to Markov chains

(GS) Chapter 11.1

Tue. 15 Sep.

10:00 - 11:45

Exercise session

Rooms ES61, ES62, ES63

VLE


Wed. 16 Sep.

10:00 - 11:45

Lecture

Room HC2

Introduction to Poisson processes

(MA) Chapters 3.8, 4.3

Thu. 17 Sep.

10:00 - 11:45

Exercise session

Rooms ED5217, ES61, ES62, ES63

VLE Test 1

1. Axioms of probability and general additional rule

2. Discrete probability densities and distribution functions

3. Counting combinations

4. Simple probability on cross-tabulated data

5. Continuous probability densities and distriubtion functions

6. Normal distribution

7. Expectation, variance and their properties

w39(4)


Mon. 21 Sep.

13:15 - 15:00

Lecture

Room HC2

Estimation and confidence intervals, central limit theorem

(MA) Chapters 6.1, 6.3, 7.1, Theorem 7.3.4, 7.4, 8.1, 8.2

Tue. 22 Sep.

10:00 - 11:45

Exercise session

Rooms ES61, ES62, ES63

(MA) Exercises 7.47, 7.48, 7.49, 7.53, 7.55, 7.56, 8.23, 8.24


Wed. 23 Sep.

10:00 - 11:45

Lecture

Room HC2

Confidence intervals (continued), introduction to statistical tests

(MA) Chapters 6.1, 6.3, 7.1, Theorem 7.3.4, 7.4, 8.1, 8.2

Thu. 24 Sep.

10:00 - 12:00

Exercise session

Rooms ES61, ES62, ES63

VLE


w40(5)


Mon. 28 Sep.

13:15 - 15:00

Lecture

Room HC2

Inferences on proportions

(MA) Chapters 9.1, 9.3

Tue. 29 Oct.

10:00 - 11:45

Exercise session

Rooms ES61, ES62, ES63

VLE

Wed. 30 Sep.

10:00 - 11:45

Lecture

Room HC2

Comparing two means

(MA) Chapters 10.1, 10.3, 10.4

Thu. 1 Oct.

10:00 - 11:45

Exercise session

Rooms ES61, ES62, ES63

VLE

w41(6)


Mon. 5 Oct.

13:15 - 15:00

Lecture

Room HC2

Generating functions

Tue. 6 Oct.

10:00 - 11:45

Exercise session

Rooms ES61, ES62, ES63

(EG) Exercise 6.18bc

VLE

Wed. 7 Oct.

10:00 - 11:45

Lecture

Room HC2

Moment generating functions, law of large numbers

(MA) Chapters 3.4 (m.g.f. sec.), 7.3

(GS) Chapter 8

Thu. 8 Oct.

10:00 - 11:45

Exercise session

Rooms ES61, ES62, ES63

(A) Exercises 13.2.1, 13.2.3, 13.3.11, 13.3.23, 13.3.37

w42(7)


Mon. 12 Oct.

13:15 - 15:00

Lecture

Room HC2


Linear regression

(MA) Chapters 11.1, 11.2, 11.3

Tue. 13 Oct.

10:00 - 11:45

Exercise session

Rooms ES61, ES62, ES63

(MA) Exercises 3.32, 3.34

(GS) Exercises 8.1.4, 8.1.8, 8.2.1, 8.2.2, 8.2.10

Wed. 14 Sep.

10:00 - 11:45

Lecture

Room HC2

Introduction to non-parameteric tests

(MA) Chapter 10.6

Tue. 15 Oct.

10:00 - 11:45

Exercise session

Rooms ED2480, ES61, ES62, ES63

VLE

w43(8)


Mon. 19 Oct.

10:00 - 11:45

Lecture

Room HC3

TBA


Tue. 20 Oct.

10:00 - 11:45

Exercise session

Rooms ED2480, ES61, ES62, ES63

VLE Test 2

1. Central limit theorem

2. Confidence interval on the mean of a normal population with known variance,
various comprehension questions

3. The normal approximation to the binomial distribution
(the exact calculation of a binomial coefficient will be required!)

4. Confidence interval on a proportion

5. Central limit theorem for a sample mean

Wed. 21 Oct.

10:00 - 11:45

Lecture

Room HA4

Consultation


w44(9)


Tue. 27 Oct.

Written Exam







Recommended exercises for self study
Week Theme Exercises

36(1)

Interpreting probabilities (MA 1.1)

Sample spaces and events (MA 1.2)

Permutations and combinatorics (MA 1.3)

Axioms of probability (MA 2.1)

Conditional probability (MA 2.2)

Independence of the multiplication rule (MA 2.3)

Bayes' theorem (MA 2.4)

Dicrete probability densities (MA 3.2)

Expectation and distribution parameters (MA 3.3)

Geometric distribution (MA 3.4)

Binomial distribution (MA 3.5)

1.4

1.5, 1.6, 1.7

1.11, 1.12, 1.13, 1.14, 1.21, 1.24, 1.27

2.3, 2.4, 2.5, 2.6, 2.11

2.13, 2.14, 2.16, 2.39

2.19, 2.26, 2.40

2.36, 2.41

3.7, 3.9, 3.10, 3.13

3.14, 3.16, 3.17, 3.20, 3.21

3.24(abc), 3.31

3.41, 3.42

37(2)

Continuous densities (MA 4.1)

Expectation and distribution parameters (MA 4.2)

Normal distribution (MA 4.4)

Normal probability rule and Chebyshev's inequality (MA 4.5)

Normal approximation to the binomial distribution (MA 4.6)

Joint densities and independence (MA 5.1)

Expectation and covariance (MA 5.2)

Correlation (MA 5.3)

4.1, 4.3, 4.5, 4.6, 4.9, 4.12, 4.71

4.15, 4.17, 4.18, 4.19, 4.22, 4.70

4.41, 4.43

4.47, 4.48, 4.49

4.52, 4.57

5.1, 5.3, 5.5, 5.9, 5.12

5.16, 5.21, 5.24, 5.25, 5.26

5.29, 5.30, 5.33

38(3)

Markov chains (GS 11.1)

Absorbing markov chains (GS 11.2)

Poisson distribution (MA 3.8)

Exponential distribution (MA 4.3)

11.1.1, 11.1.8, 11.1.9, 11.1.10, 11.1.19

11.2.1, 11.2.2, 11.2.3

3.47, 3.48

4.34, 4.35, 4.36, 4.37

39(4)

Random sampling (MA 6.1)

Sample statistics (MA 6.3)

Distribution of sample mean (MA 7.3)

Interval estimation and central limit theorem (MA 7.4)

Interval estimation of variability (MA 8.1)

Estimating the mean and the Student's t-distribution (MA 8.2)

Hypothesis testing (MA 8.3)

6.1, 6.4

6.17, 6.24 (b, c, d, e)

7.44, 7.45, 7.46

7.49, 7.50

8.1, 8.2, 8.3, 8.5

8.10, 8.12, 8.13, 8.17

8.21, 8.24

40(5)

Estimating proportions (MA 9.1)

Comparing two proportions (MA 9.3)

Point estimation: independent samples (MA 10.1)

Comparing means: variance equal (MA 10.3)

Comparing means: variance unequal (MA 10.4)

9.1, 9.2, 9.4, 9.8

9.19, 9.20, 9.21, 9.23

10.1, 10.3, 10.4

10.12, 10.14, 10.16, 10.17, 10.18, 10.19

10.21, 10.23, 10.24, 10.26, 10.28

41(6)

(A 13.2)

(A 13.3)

Moment generating function (MA 3.4)

Distribution of sample mean (MA 7.3)

13.2.7, 13.2.9

13.3.13, 13.3.35, 13.3.21

3.31, 3.35

7.38, 7.45

42(7)

Model and parameter estimation (MA 11.1)

Properties of least-squares estimators (MA 11.2)

Confidence interval estimation (MA 11.3)

Alternative nonparametric methods (MA 10.6)

11.1, 11.7, 11.10

11.11, 11.12

11.16, 11.20, 11.23

10.37, 10.38, 10.39


Computer labs
The computer labs will be based on Mathematical Sciences department's Stats VLE.

Stats VLE is a web-based system providing you with all the 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.
You may re-run the question-solution cycle as many times as you feel necessary to deepen your 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.
Before starting a new theme you must read and learn the corresponding chapter in the Guide.

There are assisted lab sessions and where you can bring all the questions which you could not solve by your own.
This organisation assumes you have already done the reading and attempted questions before you may bring your problems to discussion with the teaching team.

How to get started

    1. You need to register first to be able to use the VLE.
    Ensure that you have a Swedish Person Number (personnummer), university login and password and a valid Chalmers or GU email address.
    2. Visit http://vle.math.chalmers.se, press Register button on the login page and fill in the required details.
    3. Shortly after completion of the registration process a password will be sent to the Chalmers email address you specified at the registration which must be in the domains student.chalmers.se or student.gu.se!
    4. Retrieve the password from the received email and log in with it. Once you are in, select MVE055 course and click Update registrations.
    There are four alternative one-hour computer lab sessions on Tuesday at 10 and 11am or Thursday at 10 and 11am.
    You need to come to only one of these. So click on the one you prefer.
    However the amount of available computers is such that you should be able (if you wish) to attend all of the sessions.
    Similarly, make a choice for a test sessions. Now you should be brought to your main VLE page, so proceed to Methods section.
    Take time to explore VLE's interface.
    5. The first thing that you might notice is that there is a very large number of exercises and that this will be impossible for you to do them all in the given time.
    Firstly some exercises are doubled as they are both in English and Swedish and also you are not expected to do them all.
    Do the exercises until you are comfortable with the topic! The other thing is that you need to do your calculations in some software.
    You may choose whichever one you like however the suggested software is matlab or R.

Note that the tests and examination will consist of similar questions in a similar interface, so learn with Stats VLE and Have fun!

Course requirements
The course is intended for 2nd year Computer Sciense students. More information about the course can be found here.
Assignments
Assignments 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.

Assignment
Date of issue
Deadline
E-mail subject

Skiplistor

Mon. 7 Sep.

Mon. 21 Sep.

MVE055, 2015, Skiplistor

Penney's game

Mon. 21 Sep.

Mon. 5 Oct.

MVE055, 2015, Penney's game

Statistisk undersökning

Mon. 28 Sep

Mon. 12 Oct

MVE055, 2015, Statistic undesökning


Examination
The grade for the examination consists of two parts, the home assignments and exam.
To pass the course one has to hand-in all three home assignments and pass the exam.
The exam consists of three parts, two VLE tests on the 17th of September and 20th of October and the final written exam.
The final written exam will give a maximal score of 30 points.
The Chalmers grading scale is 12-17.5: 3; 18-23.5: 4; 24-30: 5.
The GU grading scale is 12-21.5: G; 22-30: VG.
There is a possibility to obtain bonus points by taking VLE tests: each of two VLE test gives a maximum of 3 bonus points.
The bonus points will be added to your score from the exam before the grade is computed.
NOTE: In order to pass the course, you must obtain at least 9 points on the written final exam.
The final grade will be as follows,

Points Percentage
Grade

[12 - 18)

40% - 60%

3

[18 - 24)

60% - 80%

4

[24 - 30]

80% - 100%

5


Examination procedures
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.
At the exam, you should be able to show valid identification.
Before the exam, it is important that you report that you want to take the examination. You can do this by the Chalmers Student Portal.
Notice of result is obtained only by email via Ladok. (Not verbally at study expedition.) This is done automatically when the results are registered. Check that you have the right grades and score.

At the annual examination:
When it is practical a separate review is arranged. The date of the review will be announced here on the course website. Anyone who can not participate in the review may thereafter retrieve and review their exam on Mathematical sciences study expedition, Monday through Friday, from 9:00 to 13:00. Any complaints about the marking must be submitted in writing at the office, where there is a form to fill out.

At re-examination:
Exams are reviewed and picked up at the Mathematical sciences study expedition, Monday through Friday, from 9:00 to 13:00. Any complaints about the marking must be submitted in writing at the office, where there is a form to fill out.
Old exams
The "old style" exams are available on the previous year's course web-page.

2014-10-28

English

Solution

2014-08-27

English

Solution

2014-01-13

English

Solution

2013-10-22

English

Solution

2013-08-28

English

Solution

2013-01-15

English

Solution

2012-10-20

English Swedish

Solution

2012-01-11

English Swedish

Solution

2011-10-18

English Swedish

Solution