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## Syllabus for

LMA201 - Statistics with applications

Owner: TIELL
7,5 Credits
Grading: TH - Five, Four, Three, Fail
Education cycle: First-cycle
Major subject: Mathematics
Department: 11 - MATHEMATICAL SCIENCES

Teaching language: Swedish
Application code: 63121
Open for exchange students: No
Maximum participants: 50
Only students with the course round in the programme plan

 Module Credit distribution Examination dates Sp1 Sp2 Sp3 Sp4 Summer course No Sp 0116 Examination 7,5c Grading: TH 7,5c 16 Mar 2020 am L, 08 Jun 2020 pm L, 27 Aug 2020 am L

#### In programs

TIELL ELECTRICAL ENGINEERING, Year 2 (compulsory)
TIDAL COMPUTER ENGINEERING, Year 3 (compulsory elective)
TIDAL COMPUTER ENGINEERING, Year 2 (elective)

Johan Tykesson

#### Replaces

LMA200   Mathematical statistics

#### Eligibility:

In order to be eligible for a first cycle course the applicant needs to fulfil the general and specific entry requirements of the programme(s) that has the course included in the study programme.

#### Course specific prerequisites

Basic courses in Linear algebra and Calculus.

#### Aim

The aim of the course is to give students knowledge of basic probability theory and statistical methods used in engineering and science. The applied parts of the course are in statistical design of experiments and statistical quality control. Moreover, students gain basic knowledge about Markov chains.

#### Learning outcomes (after completion of the course the student should be able to)

• explain how different situations are influenced by chance
• perform basic risk calculations using some known probability distributions
• calculate quantities such as mean, median, quartile, percentile, standard deviation, variance and interquartile
• make probability calculations in more complex situations, requiring sums and linear combinations of random variables, and be able to use the central limit theorem and some other approximations
• draw conclusions from investigations by calculating confidence intervals for the expected value and the standard deviation
• use Markov chains in discrete and continuous time to, for example, assess the reliability of a connected system.
• explain how to examine how different factors interact and affect the result by performing factorial experiments

#### Content

The course is structured so that it starts with basic probability theory. This is followed by  random variables and the common probability distributions with mean values ​​and variances, functions of random variables and the central limit theorem. The topic inference covers interval estimation. Next the course deals with statistical experimental design with factorial and reduced factorial designs. The course ends with Markov chains in discrete and continuous time

The course includes the following elements:

Probability:

Basic probability concepts
Dependent and independent events
Combinatorics
Random variables and their expected values ​​and variances
The discrete probability distributions general, uniform, hypergeometric, binomial and Poisson distribution
The continuous probability distributions general, rectangle-, exponential, Weibull-, normal, t- and Chi2- distribution
Functions and sums of random variables
Central limit theorem

#### Statistical inference:

Point estimation, interval estimation

#### Statistical design of experiments:

Factorial experiments
Reduced factorial experiments
Blocking

#### Markov Chains:

Transition probabilities
Absorbent state
Stationary distributions
Reliability of connected systems

#### Organisation

The course includes approximately 28 lectures and 7 practice sessions where lectures are mixed with problem solving sessions and one laboratory work in the field of experimental design.

#### Literature

See the course web page

#### Examination including compulsory elements

The examination is based on a written exam and an approved laboration. Maximum number of points on the exam is 50. For grade 3 the limit is 20 points on the written exam, grade 4 requires at least 30 points on the exam, and grade 5 at least 40 points on the exam.

Published: Wed 26 Feb 2020.