# Mathematical Statistics, 6 credits (TAMS27)

Matematisk statistik, 6 hp

### Main field of study

Mathematics Applied Mathematics

First cycle

Programme course

Jörg-Uwe Löbus

### Director of studies or equivalent

Ingegerd Skoglund
Course offered for Semester Period Timetable module Language Campus VOF
6CDDD Computer Science and Engineering, M Sc in Engineering 4 (Spring 2017) 2 2 Swedish Linköping o

### Main field of study

Mathematics, Applied Mathematics

First cycle

G2X

### Course offered for

• Computer Science and Engineering, 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

Series, Integral calculus (one and two variables), Linear algebra, differential calculus.

### Intended learning outcomes

The course gives an introduction to mathematical modelling of experiments where the outcome is influenced by random factors. It is directed towards topics required for application in computer engineering. By the end of the course, the student should

• understand basic concepts in probability theory
• be able to set up relevant probability models for random experiments
• apply the techniques in the course to analyse these models

### Course content

Sample space, events and probabilities. Elementary combinatorial probability. Conditional probability and independence. Discrete random variables and probability distributions, expectation and variance. Binomial, Poisson distributions etc. The Probability Generating Function. Continuous Random Variables. Uniform, Exponential and Normal Distributions. Functions of random variables. Moment Generating Function. Simulating a Random Variable. Sampling. The Law of Large Numbers. The Central Limit Theorem. Stochastic Processes: The Poisson Process, introduction to Markov chains.

### Teaching and working methods

Teaching consists of lectures, tutorials and a computer laboratory.

### Examination

 TEN2 Written examination U, 3, 4, 5 6 credits

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

### Other information

 Supplementary courses: The course prepares the student for courses in:  Queueing Theory, which develops the queueing models and their applications.  Bayesian Networks, which discusses graphical modelling and algorithms for updating probabilities in causal networks.

### Department

Matematiska institutionen

### Director of Studies or equivalent

Ingegerd Skoglund

Jörg-Uwe Löbus

### Course website and other links

http://courses.mai.liu.se/GU/TAMS27

### Education components

Preliminary scheduled hours: 47 h
Recommended self-study hours: 113 h

### Course literature

Sheldon Ross: A First Course in Probability, Pearson International Edition. Exempelsamling utgiven av institutionen. Institutionens formelsamling i matematisk statistik. [Handbook of formulas published by the department.]
Sheldon Ross: A First Course in Probability, Pearson International Edition. Exempelsamling utgiven av institutionen. Institutionens formelsamling i matematisk statistik. [Handbook of formulas published by the department.]