Course syllabus for Statistics with applications

Course syllabus adopted 2021-02-26 by Head of Programme (or corresponding).

Overview

  • Swedish nameTillämpad matematisk statistik
  • CodeLMA201
  • Credits7.5 Credits
  • OwnerTIELL
  • Education cycleFirst-cycle
  • Main field of studyMathematics
  • DepartmentMATHEMATICAL SCIENCES
  • GradingTH - Pass with distinction (5), Pass with credit (4), Pass (3), Fail

Course round 1

  • Teaching language Swedish
  • Application code 63122
  • Maximum participants90
  • Open for exchange studentsNo
  • Only students with the course round in the programme overview.

Credit distribution

0116 Examination 7.5 c
Grading: TH		0 c0 c7.5 c0 c0 c0 c

In programmes

Examiner

Eligibility

General entry requirements for bachelor's level (first cycle)
Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.

Specific entry requirements

The same as for the programme that owns the course.
Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.

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.

The course examiner may assess individual students in other ways than what is stated above if there are special reasons for doing so, for example if a student has a decision from Chalmers on educational support due to disability.