Credits: 5

Schedule: 02.01.2017 - 15.02.2017

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.

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):

https://mycourses.aalto.fi/course/search.php?search=MS-A0503

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.