| TNIU66 |
Statistics and Probabillity, 6 ECTS credits.
/Statistik och sannolikhetslära/
For:
BI
FT
SL
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Prel. scheduled
hours: 42
Rec. self-study hours: 118
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Area of Education: Science
Main field of studies: Mathematics, Applied Mathematics
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Advancement level
(G1, G2, A): G1
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Aim:
The course aims to provide an introduction to mathematical modeling of random trials and to statistical methods and concepts. It shall also demonstrate applications relevant to the programs for which it is given. After the course the student will be able to:
analyze the distribution of a dataset for the central value and dispersion, such as mean, median and standard deviation, and visualize this.
describe different approaches to the concept of probability.
calculate probabilities of events, using concepts and tools such as independence, conditioning, incompatibility, complement event, union, intersection, combinatorics, tree diagram.
formulate a probabilistic model using random variables, also with the central limit theorem, and use it to determine the characteristics of its distribution and calculate probabilities.
calculate point estimates of expected value, variance , standard deviation, probability and intensity, and assess their suitability.
calculate confidence intervals for the expected value (with and without a known standard deviation), probability and intensity, and interpret the results.
formulate and implement hypothesis testing, and therein interpret the concepts of strength functions and P-value.
conduct a correlation analysis and interpret the results.
set up and interpret a linear regression model with two variables, determine whether a linear model is applicable and assess the reliability of estimates of both expected values �?<�?
use computer support for all calculations where relevant.
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Prerequisites: (valid for students admitted to programmes within which the course is offered)
A first course in mathematics at university level.
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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Supplementary courses:
Courses in simulation, quantitative logistics etc.
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Organisation:
Teaching is done in lectures, problem classes and laboratory work.
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Course contents:
- Probability: the concepts of probability. Sample space and event. Set theory and combinatorics. Conditional probabilities, Bayes' Theorem and the concept of independent events. Discrete and continuous random variables with distribution measures such as expected value, variance / standard deviation, covariance and correlation. The most common probability models, including uniform, binomial, poisson, exponential and normal distribution model. The Central Limit Theorem.
- Statistics: Descriptive statistics with the concepts of mean, median and standard deviation, and visualizations. Point and interval estimates of the expected value (with and without a known standard deviation), probability and intensity. Point estimation of variance and standard deviation. Hypothesis testing, including P-value and intensity function. Correlation. Linear regression for two variables, including control of suitablitity and determination of confidence and prediction intervals.
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Course literature:
Gunnar G. Lövås, Statistik - metoder och tillämpningar, Liber AB, Malmö, 2006.
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Examination: |
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Written examination
Laboratory work
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4,5 ECTS
1,5 ECTS
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Course language is Swedish.
Department offering the course: ITN.
Director of Studies: George Baravdish
Examiner: Michael Hörnquist
Link to the course homepage at the department
Course Syllabus in Swedish
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