Please note! Course description is confirmed for two academic years, which means that in general, e.g. Learning outcomes, assessment methods and key content stays unchanged. However, via course syllabus, it is possible to specify or change the course execution in each realization of the course, such as how the contact sessions are organized, assessment methods weighted or materials used.


After course the student
- can compute probabilities of composite events by applying operations of set theory
- is familiar with the most important discrete and continuous probability distributions and recognizes situations that can modeled with them
- can apply joint distributions to compute statistics of random vectors and to recognize when two random variables are stochastically independent
- knows methods for estimating the parameters of a statistical model
- can compute posterior distributions and make conclusions based on them
- can explain what can and what cannot be concluded from a p-value of chosen statistical test

Credits: 5

Schedule: 11.01.2021 - 24.02.2021

Teacher in charge (valid 01.08.2020-31.07.2022): Jukka Kohonen

Teacher in charge (applies in this implementation): Jukka Kohonen

Contact information for the course (applies in this implementation):

CEFR level (applies in this implementation):

Language of instruction and studies (valid 01.08.2020-31.07.2022):

Teaching language: English

Languages of study attainment: English


  • Valid 01.08.2020-31.07.2022:

    - the notion of probability and its basic arithmetic rules
    - the most important discrete and continuous distributions
    - expectation, sample mean, and the law of large numbers
    - variance, sample variances, and normal approximation
    - stochastic dependence and correlation
    - description of data using statistics and histograms
    - parameter estimation of statistical models
    - the concept of a confidence interval
    - prior distribution, likelihood function, and posterior distribution
    - testing of simple statistical hypotheses

Assessment Methods and Criteria
  • Valid 01.08.2020-31.07.2022:

    lectures, exercises, midterm exams/final exam.

  • Applies in this implementation:

    Exercises account for 40% and exam for 60% of total points.

    It is also possible to pass the course by exam only.

  • Valid 01.08.2020-31.07.2022:

    Participating in lectures 24 h (4 h/week)
    Participating in exercises classes 24 h (4 h/week)
    Weekly independent study 36-72 h (6-12 h/week)
    Participating and preparing for exams 4-40 h


Study Material
  • Valid 01.08.2020-31.07.2022:

    Sheldon M Ross, Introduction to Probability and Statistics for Engineers and Scientists (5th ed), Academic Press 2014 (available online via Aalto network).

  • Applies in this implementation:

    Course material includes also lecture slides, exercises and exercise solutions.

Substitutes for Courses
  • Valid 01.08.2020-31.07.2022:

    Substitutes the courses Mat-1.2600 and Mat-1.2620 and the courses MS-A050X First course in probability and statistics, MS-A0510 Mathematics 3.

  • Valid 01.08.2020-31.07.2022:

    University level mathematics course, for example MS-A000X Matrix algebra or MS-A010X Differential and integral calculus 1.