MATA280 Foundations of stochastics (5 cr)

Study level:
Intermediate studies
Grading scale:
0-5
Language:
English, Finnish
Responsible organisation:
Department of Mathematics and Statistics
Curriculum periods:
2024-2025, 2025-2026, 2026-2027, 2027-2028

Description

The distribution of a discrete random variable, probability generating function and moments. Random vectors, independence, and the product measure of countable spaces. Markov and Chebyshev inequalities, stochastic convergence of random variables, and weak law of large numbers. The most common discrete probability distributions.

Learning outcomes

The course introduces the basic concepts of probability theory and discrete random variables. During the course, the student develops his or her analytical reasoning skills and, in addition, learns to share the results of his or her own reasoning with others.

After completing the course, the student

  • identifies the most common discrete probability distributions,
  • knows how to use the probability generating function to calculate descriptive statistics of random variables,
  • knows what is the joint distribution and the boundary distribution of a random vector and is able to determine if the components of the random vector are independent,
  • can explain how and when the sum of random variables can be estimated using its expected value,
  • has learned how to simulate the paths of a simple random process on a computer.

Additional information

28h lectures, 7 exercise sessions

Description of prerequisites

Basics of sequences, series and power series (for example MATA172 Introduction to mathematical analysis 2 and MATP213 Calculus 3).

Study materials

  • Meester: A natural introduction to probability theory, chapters 1-2 and 4.1.
  • Ross: A first course in probability, chapters 1-4, 6.1-6.4, 7.1-7.6 and 8.1-8.2 for discrete random variables.

Literature

  • Meester, R., A natural introduction to probability theory, Birkhäuser, 2003.
  • Ross, S., A first course in probability, Pearson, 2010, 8. painos.

Completion methods

Method 1

Evaluation criteria:
Opintojakson arvosana määräytyy kurssitentin pistemäärän ja laskuharjoituspisteiden sekä mahdollisesti harjoitustyön arvosanan perusteella.
Time of teaching:
Period 2
Select all marked parts

Method 2

Evaluation criteria:
The grade is based on the number of points in the final exam.
Select all marked parts
Parts of the completion methods
x

Teaching (5 cr)

Type:
Participation in teaching
Grading scale:
0-5
Language:
Finnish

Teaching

x

Exam (5 cr)

Type:
Exam
Grading scale:
0-5
Language:
English, Finnish
No published teaching