Course information
Learning outcomes
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
- can use a computer to investigate data sets and probability distributions
Content
- 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
Teacher
Jukka Kohonen
Study material
Sheldon M Ross, Introduction to Probability and Statistics for Engineers and Scientists (5th ed), Academic Press 2014 (available online via Aalto network).
Workload
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
Prerequisites
Recommended prerequisites: University level mathematics course, for example MS-A000X Matrix algebra or MS-A010X Differential and integral calculus 1.
Evaluation
lectures, exercises and course exam OR exam only
Teaching time and location
The teaching time and the location of the course can be found at Sisu information system
- The link leads to Completion methods tab of the course page
- From the top of the page (Version drop-down menu), check that academic year 2025-2026 is selected
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From the blue bar, click Lecture and open the Groups and teaching times tab to see the teaching time and the location of the course. Exam times can be seen by clicking Exam.
Exam instructions at the Open University
The teacher has four (4) weeks to grade the exam submissions starting from the exam date.
Further information
Equivalences to other courses: 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.
Online learning environment for the course
MyCourses online learning environment is a tool for both students and teachers for communication and managing everyday course work. You need an Aalto User ID to log in to the course's MyCourses workspace and participate in teaching.
Digital workspace of the course:
MyCourses
More details on completing the course will be available at MyCourses closer to the start of the course.
Registration and course fee
Registration for Open University courses is done via the link below:
Course registration
Registration for this course starts on 8.12.2025 at 9.00
Registration for this course ends on 12.1.2026 at 23.59
It is not possible to register before the registration period has started or after it has ended.
The number of participants is limited to 5.
This course is organized by the Aalto University School of Science.
The course fee is paid upon registration for each course at a time and it is binding. Familiarize yourself with registration and payment rules as well as other guidelines for students:
Registration, payments and rules
Activating Aalto ID and Multifactor Authentication
You can activate your Aalto User ID the day after the registration and you should activate it no later than the day before the start of the course.
Instructions for activating your Aalto user ID
Once you have activated your Aalto user ID, also enable multifactor authentication. Some of Aalto University's services require multifactor authentication.
Instructions for using Multifactor Authentication
