Probability and Statistics, first course, 6 credits (TAMS11)

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

UPGA	Exercise	U, G	1 credits
TENB	Written Examination	U, 3, 4, 5	5 credits

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