# Probability, First Course, 4 credits (TAMS36)

Sannolikhetslära, 4 hp

### Main field of study

Mathematics Applied Mathematics

First cycle

Programme course

### Examiner

Torkel Erhardsson

### Director of studies or equivalent

Ingegerd Skoglund
Course offered for Semester Period Timetable module Language Campus VOF
6CITE Information Technology, M Sc in Engineering 4 (Spring 2017) 2 4 Swedish Linköping o

### Main field of study

Mathematics, Applied Mathematics

First cycle

G1X

### Course offered for

• Information Technology, M Sc in Engineering

### 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

Calculus, algebra, differential and integral calculus, power series.

### Intended learning outcomes

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 influence may affect the results.
• construct relevant probabilistic models for simple random experiments.
• describe basic concepts and theorems of probability theory, e.g., random variable, distribution function and the law of total probability.
• compute important quantities in probabilistic models, e.g., probabilities and expectations.

### Course content

• Definition of probability
• Combinatorial methods
• Conditional probability and Bayes rule
• Discrete random variables, probability function, cumulative distribution function.
• Expected value, variance, covariance, correlation
• Special examples: Bernoulli, Binomial, Geometric, Hypergeometric, Negative Binomial, Poisson, and applications.
• Joint probability functions, conditional probability function, conditional expectation.
• Continuous random variables
• Special distributions: the exponential distribution, the normal distribution.
• Sampling and the Central Limit Theorem.
• The Poisson Process and applications.
• Scenarios illustrating applications of probability and statistics.

### Teaching and working methods

Teaching consists of lectures and lessons dealing with theory and exercises together with work in PBL-group.

### Examination

 BAS1 Tutorial work U, G 1 credits TEN1 Written examination U, 3, 4, 5 3 credits

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

### Other information

 Supplementary courses: Statistics, Digital Image Processing, Signal Theory

### Department

Matematiska institutionen

### Director of Studies or equivalent

Ingegerd Skoglund

### Examiner

Torkel Erhardsson

### Course website and other links

http://courses.mai.liu.se/GU/TAMS36

### Education components

Preliminary scheduled hours: 52 h
Recommended self-study hours: 55 h

### 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.
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.