Syllabus for |
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LMA201 - Statistics with applications
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| Tillämpad matematisk statistik |
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| Syllabus adopted 2019-02-13 by Head of Programme (or corresponding) |
| Owner: TIELL |
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7,5 Credits
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| Grading: TH - Pass with distinction (5), Pass with credit (4), Pass (3), Fail |
| Education cycle: First-cycle |
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Major subject: Mathematics
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Department: 11 - MATHEMATICAL SCIENCES
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Teaching language: Swedish
Application code: 63127
Open for exchange students: No
Maximum participants: 90
Only students with the course round in the programme plan
| Module |
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Credit distribution |
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Examination dates |
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Sp1 |
Sp2 |
Sp3 |
Sp4 |
Summer course |
No Sp |
| 0116 |
Examination |
7,5 c |
Grading: TH |
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7,5 c
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15 Mar 2021 am L, |
08 Jun 2021 pm L, |
26 Aug 2021 pm L |
In programs
TIELL ELECTRICAL ENGINEERING, Year 2 (compulsory)
TIDAL COMPUTER ENGINEERING - AI - Machine learning , Year 2 (compulsory)
TIDAL COMPUTER ENGINEERING - Common branch of study, Year 3 (compulsory elective)
Examiner:
Johan Tykesson
Go to Course Homepage
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.