| TAMS11 |
Probability and Statistics, First Course, 6 ECTS credits.
/Sannolikhetslära och statistik, grundkurs/
For:
DAV
DI
DPU
EL
EM
FyN
KA
M
MEC
PRO
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Prel. scheduled
hours: 56
Rec. self-study hours: 104
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Area of Education: Science
Main field of studies: Mathematics, Applied Mathematics
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Advancement level
(G1, G2, A): G2
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Aim:
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.
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Prerequisites: (valid for students admitted to programmes within which the course is offered)
Analysis, algebra, differential and integral calculus, power series and differential equations.
Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshhold requirements for progression within the programme, or corresponding.
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Organisation:
Teaching consists of lectures, lessons and obligatory computer exercises.
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Course contents:
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.
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Course literature:
Jay L. Devore: Probability and Statistics for Engineering and the Sciences
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Examination: |
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Written examination
Computer exercises
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5 ECTS
1 ECTS
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Course language is Swedish/English.
Department offering the course: MAI.
Director of Studies: Ingegerd Skoglund
Examiner: Xiangfeng Yang
Link to the course homepage at the department
Course Syllabus in Swedish
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