Credits: 5

Schedule: 07.01.2019 - 20.02.2019

Teaching Period (valid 01.08.2018-31.07.2020): 

III Spring (2018-2019, 2019-2020)

Learning Outcomes (valid 01.08.2018-31.07.2020): 

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 the posterior distribution of a simple statistical model from a given prior distribution and observed data
- can explain what can and what cannot be concluded from a p-value of chosen statistical test

Content (valid 01.08.2018-31.07.2020): 

- 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 01.08.2018-31.07.2020): 

lectures, exercises, midterm exams/final exam.

Elaboration of the evaluation criteria and methods, and acquainting students with the evaluation (applies in this implementation): 

Weekly homework problems: 20% of the grade.

Final written exam: 80 % of the grade.

The homework problems will be reported orally during the second exercise session of the week. The student should mark which of the problems he/she has solved, and be prepared to present the solution orally in front of the class if instructed to do so. The 4 best out of the 5 exercise sheets count towards the final grade. Point obtained from the homework problems can be combined with any of the written exams during 2019.

In the written exam, no equipment will be allowed, other than calculator and ONE HAND-WRITTEN FORMULA SHEET that the student may prepare him/herself. In addition, standard tables of distribution functions will be attached to the exam.

Workload (valid 01.08.2018-31.07.2020): 

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 01.08.2018-31.07.2020): 

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

Substitutes for Courses (valid 01.08.2018-31.07.2020): 

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.

Course Homepage (valid 01.08.2018-31.07.2020):

Prerequisites (valid 01.08.2018-31.07.2020): 

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

Grading Scale (valid 01.08.2018-31.07.2020): 



Registration and further information