KURSPLAN
Probability Theory, 7,5 högskolepoäng
Probability Theory, 7.5 credits
Kursplan för studenter höst 2022
Kurskod: | FJPRT30 |
Fastställd av: | Forskarutbildningsrådet 2019-12-19 |
Gäller fr.o.m.: | Våren 2020 |
Version: | 1 |
Utbildningsnivå: | Forskarnivå |
Forskarutbildningsämne: |
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Syfte
This course gives a solid background in and understanding of important results and methods in probability theory at an advanced level. The objective of the course is to give students a solid knowledge of important theorems within probability theory. The course should also enable them to apply advanced probability theory to building probability models in applications. Finally to be able to solve complicated probabilistic problems and explain various convergence concepts in probability
Lärandemål
On completion of the course, the students will be able to:
Kunskap och förståelse
1. Demonstrate a deep understanding of important theorems within probability theory.
2. Demonstrate a deep understanding of various convergence concepts in probability theory
2. Demonstrate a deep understanding of various convergence concepts in probability theory
Färdighet och förmåga
3. To prove important theorems in probability theory
4. To solve advanced problems in probability theory
4. To solve advanced problems in probability theory
Värderingsförmåga och förhållningssätt
5. To critically apply central results in probability theory on typical probabilistic problems.
Innehåll
This course deals with random variables in one and several dimensions, conditional distributions, moment generating functions and characteristic functions, multivariate normal distributions, quadratic forms, order statistics, convergence criteria for random variables, the Borel-Cantelli lemmas, convergence via transforms, the central limit theorem and strong law of large numbers.
Undervisningsformer
The course is designed as a series of lecturers and problem-solving sessions. Grading is based on individual performance via oral presentations and written hand ins.
Undervisningen bedrivs på engelska.
Förkunskapskrav
Admitted to a doctoral program in statistics or a related subject of a recognized business school or university.
Examination och betyg
Kursen bedöms med betygen Underkänd eller Godkänd.
Course assessment consists of two elements
• Oral presentation deals with ILOs 1,2,3,4,5
• Written assignments deals with ILOs 1,2,3,4,5
Each of these two elements must be passed to obtain a pass in the course.
The grades given are pass or fail.
Course assessment consists of two elements
• Oral presentation deals with ILOs 1,2,3,4,5
• Written assignments deals with ILOs 1,2,3,4,5
Each of these two elements must be passed to obtain a pass in the course.
The grades given are pass or fail.
Kursvärdering
A course evaluation will be conducted at the end of the course.
Kurslitteratur
A. Gut, An Intermediate Course in Probability Theory, Springer-Verlag Second edition.
A. Gut, Probability: A Graduate Course Series: Springer Texts in Statistics. Second edition
A. Gut, Probability: A Graduate Course Series: Springer Texts in Statistics. Second edition