News
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.
2016-10-03: The first assignment is now corrected. You can pick it up outside room L3070.
2016-10-12: The second assignment is now corrected. You can pick it up outside room L3070.
2016-10-23: The third assignment is now corrected. You can pick it up outside room L3070.
Teachers
Lecturer: Roza Maghsood
Teaching Assistant: Marco Longfils, Olof Elias
Student representatives
Course reps: ALEXANDER ANDERSSON, ANTON FREDRIKSSON, MATTIAS GUSTAFSSON, DAVID OLSSON and ANGELICA STRANDBERG
Course literature
(MA) J. Milton, J. Arnold Introduction to Probability and Statistics McGraw-Hill (Course textbook)
(GS) C. Grinstead, J Snell Introduction to Probability AMS ( Available online )
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
w35(1)


Mon. 29 Aug.

13:15 - 16:00

Lecture

Room HC2

Introduction to the course

Basic definitions and probability laws

(MA) Chapters 1, 2

Tue. 30 Aug.

10:00 - 11:45

Exercise session

Rooms ML11, ML12

(MA) Chapters 1, 2

Wed. 31 Aug.

10:00 - 11:45

Lecture

Room HC2

Discrete random variables

(MA) Chapters 3.1 - 3.5

Thu. 1 Sep.

10:00 - 11:45

Exercise session

Rooms ML2, ML3

(MA) Chapters 3.1 - 3.5

w36(2)


Mon. 5 Sep.

13:15 - 15:00

Lecture

Room HC2

Continuous random variables

(MA) Chapters 4.1, 4.2, 4.4 - 4.6

Tue. 6 Sep.

10:00 - 11:45

Exercise session

Rooms ML11, ML13

(MA) Chapters 4.1, 4.2, 4.4 - 4.6

Wed. 7 Sep.

10:00 - 11:45

Lecture

Room HC2

Joint probability distributions

(MA) Chapters 5.1 - 5.3

Thu. 8 Sep.

10:00 - 11:45

Exercise session

Rooms ML11, ML13

(MA) Chapters 5.1 - 5.3

w37(3)


Mon. 12 Sep.

13:15 - 15:00

Lecture

Room HC2

Introduction to Markov chains

(GS) Chapter 11.1

Tue. 13 Sep.

10:00 - 11:45

Exercise session

Rooms ML11, ML13

(GS) Chapter 11.1


Wed. 14 Sep.

10:00 - 11:45

Lecture

Room HC2

Introduction to Poisson processes

(MA) Chapters 3.8, 4.3

Thu. 15 Sep.

10:00 - 11:45

Exercise session

Rooms ML3, ML4

(MA) Chapters 3.8, 4.3


w38(4)


Mon. 19 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. 20 Sep.

10:00 - 11:45

Exercise session

Rooms EL42, ML13

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


Wed. 21 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. 22 Sep.

10:00 - 12:00

Exercise session

Rooms EL41, EL43

(MA) Chapters 6.1, 6.3, 7.1


w39(5)


Mon. 26 Sep.

13:15 - 15:00

Lecture

Room HC2

Inferences on proportions

(MA) Chapters 9.1, 9.3

Tue. 27 Oct.

10:00 - 11:45

Exercise session

Rooms ML13, ML14

(MA) Chapters 9.1, 9.3

Wed. 28 Sep.

10:00 - 11:45

Lecture

Room HC2

Comparing two means

(MA) Chapters 10.1, 10.3, 10.4

Thu. 29 Sep.

10:00 - 11:45

Exercise session

Rooms ML2, ML3

(MA) Chapters 10.1, 10.3, 10.4

w40(6)


Mon. 3 Oct.

13:15 - 15:00

Lecture

Room HC2

Moment generating function

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

Tue. 4 Oct.

10:00 - 11:45

Exercise session

Rooms ML13, ML14

(MA) Chapters 3.4

Wed. 5 Oct.

10:00 - 11:45

Lecture

Room HC2

law of large numbers

(MA) Chapters 7.3

(GS) Chapter 8

Thu. 6 Oct.

10:00 - 11:45

Exercise session

Rooms ML11, ML12

TBA

w41(7)


Mon. 10 Oct.

13:15 - 15:00

Lecture

Room HC2


Linear regression

(MA) Chapters 11.1, 11.2, 11.3

Tue. 11 Oct.

10:00 - 11:45

Exercise session

Rooms ML11, ML12

(MA) Exercises 3.32, 3.34

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

Wed. 12 Oct.

10:00 - 11:45

Lecture

Room HC2

Introduction to non-parameteric tests

(MA) Chapter 10.6

Tue. 13 Oct.

10:00 - 11:45

Exercise session

Rooms EL41, EL43

(MA) Chapter 10.6

w42(8)


Mon. 17 Oct.

13:15 - 15:00

Lecture

Room HC2

TBA


Tue. 18 Oct.

10:00 - 11:45

Exercise session

Rooms FL71, FL72

(MA) Chapter 10.6

Wed. 19 Oct.

10:00 - 11:45

Lecture

Room HC2

Consultation


w43(9)


Tue. 25 Oct.

Written Exam







Recommended exercises for self study
Week Theme Exercises

35(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

36(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

37(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

38(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

39(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

40(6)

Moment generating function (MA 3.4)

Distribution of sample mean (MA 7.3)

3.31, 3.35

7.38, 7.45

41(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


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 three.
For each assignment you have to hand in a report. The reports are to be written in English.
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
Deadline
E-mail subject

Assignment 1

Mon. 19 Sep.

MVE055, 2016, Assignment 1

Assignment 2

Mon. 3 Oct.

MVE055, 2016, Assignment 2

Assignment 3, Wine_data

Mon. 17 Oct

MVE055, 2016, Assignment 3


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 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.
Examination procedures
On the written exam you will be allowed to have a Chalmers approved calculator (Casio FX82..., Texas TI30... and Sharp ELW531...) 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.

2016-10-25

English

Solution

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