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Matematiska institutionen

Matematisk statistik

Course information, HT 2019

MAI0074 Probability theory, part 1 (graduate course)

Contents

Measure-theoretic foundations of probability theory; probability distributions; random variables; expectation; convergence concepts; laws of large numbers; characteristic functions; central limit theorems; conditional expectation and regular conditional distributions.Course literature

Durrett, R. (2019). *Probability: theory and
examples*, 5th ed. Cambridge University Press.

**Organisation**

Lectures.

Examination

Home assignments.

Teacher

Lecturer and examiner: Torkel Erhardsson. Tel nr: 281478, email: torkel.erhardsson@liu.se

Lecture plan

Lectures will be given in Hopningspunkten (MAI, House B, ground floor), unless otherwise indicated.Number of lectures: 12.

Lecture plan, with corresponding sections of Durrett, 5th ed., indicated.

L 1 (16/9, 10.15): 1.1-2, A.1-2.

L 2 (23/9, 15.15): 1.3-4.

L 3 (30/9, 8.15): 1.5-6.

L 4 (11/10, 13.15): 1.7, 2.1.

L 5 (18/10, 15.15): 1.7, A.3.

L 6 (25/10, 15.15): 2.2-3.

L 7:(1/11, 15.15): 2.4-5.

L 8:(8/11, 15.15): 3.1-2.

L 9:(15/11, 15.15): 3.3.1-3.

L 10:(22/11, 15.15): 3.4.1-2, 3.4.4.

L 11:(29/11, 15.15): 3.6, 3.8-10.

L 12:(6/12, 15.15): A.4, 4.1.

**Home assignments**

The list contains 30 problems. Each solution to a problem will be marked with 1 point (satisfactory), 0.5 points, or 0 points. A total of 20 points is required for a passing grade. All solutions should be handed in (at the latest) by May 31, 2020.

The list of home assignments.