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Probability and Statistics

Title
Probability and Statistics
Semester
F2023
Master programme in
Mathematics * / Mathematical Physical Modelling * / Mathematical Computer Modelling * / Mathematical Bioscience / Physics and Scientific Modelling
Type of activity

Course

Teaching language
English
Study regulation

Read about the Master Programme and find the Study Regulations at ruc.dk

Læs mere om uddannelsen og find din studieordning på ruc.dk

REGISTRATION AND STUDY ADMINISTRATIVE
Registration

Sign up for study activities at stads selvbetjening within the announced registration period, as you can see on the Studyadministration homepage.

When signing up for study activities, please be aware of potential conflicts between study activities or exam dates.

The planning of activities at Roskilde University is based on the recommended study programs which do not overlap. However, if you choose optional courses and/or study plans that goes beyond the recommended study programs, an overlap of lectures or exam dates may occur depending on which courses you choose.

Number of participants
ECTS
5
Responsible for the activity
Carsten Lunde Petersen (lunde@ruc.dk)
Head of study
Jesper Schmidt Hansen (jschmidt@ruc.dk)
Teachers
Study administration
INM Studieadministration (inm-studieadministration@ruc.dk)
Exam code(s)
U60166
ACADEMIC CONTENT
Overall objective

The overall objective of the course in Probability and Statistics is to endow the student with a fundamental understanding of how the mathematical theory of probability and statistics is constructed, enabling the student to critically reflect on how statistical analysis of data is applied.

Detailed description of content

Probability theory as an axiomatic mathematical theory:

  • The classical mathematical formalisation and clarification of the concepts of probability.

  • This includes probability spaces, probability distribution, independence, contingent probability, probability distributions on final, countable quantities and continuous distributions on the real axis

  • The most common distributions

Statistics:

  • Resampling techniques and non-parametric statistics

  • Introduction to likelihood-based statistical inference

  • Examples

Course material and Reading list

There is no formal text-books in this course. The curriculum consists of former lecture notes which will be handed out through moodle.

Overall plan and expected work effort

The course will be planned as a mixture of lectures and solving of exercises including discussions of exercises.

The workload is 5 ECTS corresponding to 135 hours

The stipulated workload distribution is:

  • Pre-class 42 hours

  • Classes 42 hours

  • Post classes 42 hours

  • Exam preparation 10 hours.

Format
Evaluation and feedback

The course includes formative evaluation based on dialogue between the students and the teacher(s).

Students are expected to provide constructive critique, feedback and viewpoints during the course if it is needed for the course to have better quality. Every other year at the end of the course, there will also be an evaluation through a questionnaire in SurveyXact. The Study Board will handle all evaluations along with any comments from the course responsible teacher.

Furthermore, students can, in accordance with RUCs ‘feel free to state your views’ strategy through their representatives at the study board, send evaluations, comments or insights form the course to the study board during or after the course.

Programme

The course will be planned as a mixture of lectures and solving of exercises including discussions of exercises.

Class by Class program will emerge on Moodle during the course with the following themes.

Probability theory:

  • The classical mathematical formalisation and clarification of the concepts of probability.

  • This includes probability spaces, probability distribution, independence, contingent probability, probability distributions on final, countable quantities and continuous distributions on the real axis

  • The most common distributions

Statistics:

  • Resampling techniques and non-parametric statistics

  • Introduction to likelihood-based statistical inference

  • Examples

ASSESSMENT
Overall learning outcomes

After the course the student will be able to

  • compute with and understand the theory behind probability distributions, and model random phenomena using probability theory, stochastic variables and mathematical reasoning,

  • apply parametric statistics to data, in particular in formulating hypotheses, assessing estimators, computing test probabilities and interpreting the results using mathematical and statistical reasoning,

  • apply digital tools for statistical investigations, model simulation, and analysis,

  • describe and explain the mathematical structure of probability theory,

  • demonstrate in-depth understanding of how parametric statistics is built upon probability theory.

  • analyse, evaluate and formulate models of stochastic phenomena using mathematical and statistical reasoning.

  • present stochastic and statistical theories and methods in a clear and concise manner using mathematical formalism

Form of examination
Individual oral exam without time for preparation.

Time allowed for exam including time used for assessment: 30 minutes.

Permitted support and preparation materials: All.

Assessment: 7-point grading scale.
Moderation: Internal co-assessor.
Form of Re-examination
Samme som ordinær eksamen
Type of examination in special cases
Examination and assessment criteria

The students produce a portefolio consisting of 3 sets of exercises and one mini-project. All 4 can be handed-in for review by the teacher.

At the beginning of the exam the student draws a random portfolio element for presentation without further preparation. The presentation may be interrupted by clarifying questions and the presentation will be followed by a discussion and questioning with in the curriculum of the course.

The Assessement chriteria for the written part of the exam

  • compute with and understand the theory behind probability distributions, and model random phenomena using probability theory, stochastic variables and mathematical reasoning,

  • apply parametric statistics to data, in particular in formulating hypotheses, assessing estimators, computing test probabilities and interpreting the results using mathematical and statistical reasoning,

  • apply digital tools for statistical investigations, model simulation, and analysis,

  • describe and explain the mathematical structure of probability theory

  • demonstrate in-depth understanding of how parametric statistics is built upon probability theory.

  • analyse, evaluate and formulate models of stochastic phenomena using mathematical and statistical reasoning.

  • present stochastic and statistical theories and methods in a clear and concise manner using mathematical formalism

The assessment of the oral exam is based on the student’s ability to meet the criteria mentioned above and their ability to

  • clearly present and communicate the scientific content of the course

  • engage in a scientific dialogue and discussion with the assessor and co assessor

Furthermore, whether the performance meets all formal requirements in regard to both for the written og oral exam

Exam code(s)
Exam code(s) : U60166
Last changed 19/09/2022

lecture list:

Show lessons for Subclass: 1 Find calendar (1) PDF for print (1)

Monday 13-02-2023 08:15 - 13-02-2023 10:00 in week 07
Probability and Statistics (MATHBIO)

Thursday 16-02-2023 08:15 - 16-02-2023 10:00 in week 07
Probability and Statistics (MATHBIO)

Monday 20-02-2023 08:15 - 20-02-2023 10:00 in week 08
Probability and Statistics (MATHBIO)

Thursday 23-02-2023 08:15 - 23-02-2023 10:00 in week 08
Probability and Statistics (MATHBIO)

Monday 27-02-2023 08:15 - 27-02-2023 10:00 in week 09
Probability and Statistics (MATHBIO)

Thursday 02-03-2023 08:15 - 02-03-2023 10:00 in week 09
Probability and Statistics (MATHBIO)

Monday 06-03-2023 08:15 - 06-03-2023 10:00 in week 10
Probability and Statistics (MATHBIO)

Thursday 09-03-2023 08:15 - 09-03-2023 10:00 in week 10
Probability and Statistics (MATHBIO)

Monday 13-03-2023 08:15 - 13-03-2023 10:00 in week 11
Probability and Statistics (MATHBIO)

Thursday 16-03-2023 08:15 - 16-03-2023 10:00 in week 11
Probability and Statistics (MATHBIO)

Monday 20-03-2023 08:15 - 20-03-2023 10:00 in week 12
Probability and Statistics (MATHBIO)

Thursday 23-03-2023 08:15 - 23-03-2023 10:00 in week 12
Probability and Statistics (MATHBIO)

Monday 27-03-2023 08:15 - 27-03-2023 10:00 in week 13
Probability and Statistics (MATHBIO)

Thursday 30-03-2023 08:15 - 30-03-2023 10:00 in week 13
Probability and Statistics (MATHBIO)

Monday 03-04-2023 08:15 - 03-04-2023 10:00 in week 14
Probability and Statistics (MATHBIO)

Thursday 13-04-2023 08:15 - 13-04-2023 10:00 in week 15
Probability and Statistics (MATHBIO)

Monday 17-04-2023 08:15 - 17-04-2023 10:00 in week 16
Probability and Statistics (MATHBIO)

Thursday 20-04-2023 08:15 - 20-04-2023 10:00 in week 16
Probability and Statistics (MATHBIO)

Monday 24-04-2023 08:15 - 24-04-2023 10:00 in week 17
Probability and Statistics (MATHBIO)

Thursday 27-04-2023 08:15 - 27-04-2023 10:00 in week 17
Probability and Statistics (MATHBIO)

Monday 01-05-2023 08:15 - 01-05-2023 10:00 in week 18
Probability and Statistics (MATHBIO)

Thursday 04-05-2023 08:15 - 04-05-2023 10:00 in week 18
Probability and Statistics (MATHBIO)

Monday 08-05-2023 08:15 - 08-05-2023 10:00 in week 19
Probability and Statistics (MATHBIO)

Thursday 11-05-2023 08:15 - 11-05-2023 10:00 in week 19
Probability and Statistics (MATHBIO)

Monday 15-05-2023 08:15 - 15-05-2023 10:00 in week 20
Probability and Statistics (MATHBIO)

Monday 22-05-2023 08:15 - 22-05-2023 10:00 in week 21
Probability and Statistics (MATHBIO)

Wednesday 07-06-2023 08:15 - 07-06-2023 16:00 in week 23
Probability and Statistics - Exam (MATHBIO)

Tuesday 08-08-2023 08:15 - 08-08-2023 16:00 in week 32
Probability and Statistics - Reexam (MATHBIO)