| TAMS14 |
Probability, first course, 4 ECTS credits.
/Sannolikhetslära/
For:
MED
Y
Yi
|
| |
Prel. scheduled
hours: 38
Rec. self-study hours: 69
|
| |
Area of Education: Science
Main field of studies: Mathematics, Applied Mathematics
|
| |
Advancement level
(G1, G2, A): G1
|
|
Aim:
The aim of the course is to provide an introduction to the mathematical modelling of random experiments. The emphasis is on methods applicable to problems in engineering, economy and natural sciences. After completing the course the student should have the knowledge and skills required to:
- identify experimental situations where random factors may affect the results.
- construct relevant probabilistic models for simple random
experiments.
- describe the basic concepts and theorems of probability theory, such as random variable, distribution function and the law of total probability.
- compute important quantities in probabilistic models, e.g., probabilities and expectations.
- follow a basic course in statistical theory.
|
|
Prerequisites: (valid for students admitted to programmes within which the course is offered)
Linear algebra, differential and integral calculus, series.
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.
|
|
Supplementary courses:
Statistics, basic course. Stochastic Processes. Probability Theory, Second Course. Probability and Bayesian Networks. Queueing Theory. Digital Image Processing. Signal Theory.
|
|
Organisation:
Lectures and tutorials, dealing with theory and exercises.
|
|
Course contents:
Sample space, events and probabilities. Combinatorics. Conditional probabilities and independent events. Discrete and continuous random variables. Distribution functions, probability mass functions, probability density functions. Conditional distributions and independent random variables. Functions of random variables. Expectation, variance, standard deviation, covariance, correlation coefficient. Particular distributions, e.g., Gaussian, exponential, uniform, binomial and Poisson distributions. Law of large numbers and the central limit theorem. The Poisson process.
|
|
Course literature:
G. Blom, J. Enger, G. Englund, J. Grandell, L. Holst: Sannolikhetsteori och statistikteori med tillämpningar. Studentlitteratur.
Exempelsamling utgiven av institutionen.
Institutionens formelsamling i matematisk statistik.
|
|
Examination: |
|
Written examination
|
4 ECTS
|
| |
|
|
Course language is Swedish.
Department offering the course: MAI.
Director of Studies: Ingegerd Skoglund
Examiner: Torkel Erhardsson
Link to the course homepage at the department
Course Syllabus in Swedish
|
|