Probability and Statistics, first course, 6 credits

Sannolikhetslära och statistik, grundkurs, 6 hp

TAMS11

Main field of study

Mathematics Applied Mathematics

Course level

First cycle

Course type

Programme course

Examiner

Xiangfeng Yang

Director of studies or equivalent

Ingegerd Skoglund

Education components

Preliminary scheduled hours: 56 h
Recommended self-study hours: 104 h

Available for exchange students

Yes
ECV = Elective / Compulsory / Voluntary
Course offered for Semester Period Timetable module Language Campus ECV
6IDAT Computer Engineering, B Sc in Engineering (Embedded Systems) 4 (Spring 2017) 1 1 Swedish/English Linköping, Valla E
6IDAT Computer Engineering, B Sc in Engineering (Software Engineering) 4 (Spring 2017) 1 1 Swedish/English Linköping, Valla E
6CDPU Design and Product Development 4 (Spring 2017) 1 1 Swedish/English Linköping, Valla C
6CEMM Energy-Environment-Management 6 (Spring 2017) 1 1 Swedish/English Linköping, Valla C
6CMMM Mechanical Engineering, M Sc in Engineering 4 (Spring 2017) 1 1 Swedish/English Linköping, Valla C
6KFYN Physics and Nanotechnology 4 (Spring 2017) 1 1 Swedish/English Linköping, Valla C
6MPRO Protein Science, Master's programme (Internal) 2 (Spring 2017) 1 1 Swedish/English Linköping, Valla E

Main field of study

Mathematics, Applied Mathematics

Course level

First cycle

Advancement level

G2X

Course offered for

  • Computer Science, Master's Programme
  • Design and Product Development
  • Mechanical Engineering, M Sc in Engineering
  • Computer Engineering, B Sc in Engineering
  • Engineering Electronics
  • Chemical Analysis Engineering, B Sc in Engineering
  • Physics and Nanotechnology
  • Energy-Environment-Management
  • Mechanical Engineering, Master's programme
  • Protein Science, Master's programme

Entry requirements

Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshold requirements for progression within the programme, or corresponding.

Prerequisites

Analysis, algebra, differential and integral calculus, power series and differential equations.

Intended learning outcomes

The aim of the course is to give an introduction to probability and statistics, i.e. to introduce theoretical probability models and to give methods for statistical inference based on observed data. By the end of the course the student should be able to:

  • describe and use models for phenomena influenced by random factors and calculate probabilities;
  • use random variables and their properties to describe and explain random variation;
  • use an appropriate probability model to describe and analyse observed data and draw conclusions concerning interesting parameters;
  • find point estimators of parameters and analyse their properties;
  • understand the principles of statistical inference based on confidence intervals and hypothesis testing;
  • derive confidence intervals and test hypotheses using observed data, draw conclusions and describe the uncertainty.

Course content

Probability theory: Sample space, events and probabilities. Combinatorics. Conditional probabilities and independent events. Discrete and continuous random variables, their probability distributions, expectations and variances. Normal, exponential, binomial, Poisson distributions etc. The Central Limit Theorem. Statistics: Point estimation. Properties of estimators. The method of maximum likelihood, the method of moments and the least squares estimation. Confidence intervals. Testing statistical hypotheses. Simple linear regression.

Teaching and working methods

Teaching consists of lectures, lessons and obligatory computer exercises.

Examination

UPGAExercise1 creditsU, G
TENBWritten Examination5 creditsU, 3, 4, 5

Grades

Alternative-grade scale, LiU, U, 3, 4, 5

Department

Matematiska institutionen

Director of Studies or equivalent

Ingegerd Skoglund

Examiner

Xiangfeng Yang

Course website and other links

http://courses.mai.liu.se/GU/TAMS11

Education components

Preliminary scheduled hours: 56 h
Recommended self-study hours: 104 h

Course literature

Jay L. Devore: Probability and Statistics for Engineering and the Sciences
Code Name Scope Grading scale
UPGA Exercise 1 credits U, G
TENB Written Examination 5 credits U, 3, 4, 5

Regulations (apply to LiU in its entirety)

The university is a government agency whose operations are regulated by legislation and ordinances, which include the Higher Education Act and the Higher Education Ordinance. In addition to legislation and ordinances, operations are subject to several policy documents. The Linköping University rule book collects currently valid decisions of a regulatory nature taken by the university board, the vice-chancellor and faculty/department boards.

LiU’s rule book for education at first-cycle and second-cycle levels is available at http://styrdokument.liu.se/Regelsamling/Innehall/Utbildning_pa_grund-_och_avancerad_niva. 

Jay L. Devore: Probability and Statistics for Engineering and the Sciences

Note: The course matrix might contain more information in Swedish.

I = Introduce, U = Teach, A = Utilize
I U A Modules Comment
1. DISCIPLINARY KNOWLEDGE AND REASONING
1.1 Knowledge of underlying mathematics and science (G1X level)
X
X
X
TENB

                            
1.2 Fundamental engineering knowledge (G1X level)

                            
1.3 Further knowledge, methods, and tools in one or several subjects in engineering or natural science (G2X level)

                            
1.4 Advanced knowledge, methods, and tools in one or several subjects in engineering or natural sciences (A1X level)

                            
1.5 Insight into current research and development work

                            
2. PERSONAL AND PROFESSIONAL SKILLS AND ATTRIBUTES
2.1 Analytical reasoning and problem solving
X
X
X
TENB

                            
2.2 Experimentation, investigation, and knowledge discovery
X
X
TENB

                            
2.3 System thinking

                            
2.4 Attitudes, thought, and learning
X
TENB

                            
2.5 Ethics, equity, and other responsibilities
X
TENB

                            
3. INTERPERSONAL SKILLS: TEAMWORK AND COMMUNICATION
3.1 Teamwork
X
UPGA

                            
3.2 Communications
X

                            
3.3 Communication in foreign languages

                            
4. CONCEIVING, DESIGNING, IMPLEMENTING AND OPERATING SYSTEMS IN THE ENTERPRISE, SOCIETAL AND ENVIRONMENTAL CONTEXT
4.1 External, societal, and environmental context

                            
4.2 Enterprise and business context

                            
4.3 Conceiving, system engineering and management

                            
4.4 Designing

                            
4.5 Implementing

                            
4.6 Operating

                            
5. PLANNING, EXECUTION AND PRESENTATION OF RESEARCH DEVELOPMENT PROJECTS WITH RESPECT TO SCIENTIFIC AND SOCIETAL NEEDS AND REQUIREMENTS
5.1 Societal conditions, including economic, social, and ecological aspects of sustainable development for knowledge development

                            
5.2 Economic conditions for knowledge development

                            
5.3 Identification of needs, structuring and planning of research or development projects
X
X

                            
5.4 Execution of research or development projects

                            
5.5 Presentation and evaluation of research or development projects

                            

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