### MS-A0503 - First Course in Probability and Statistics, Lecture, 9.1.2023-22.2.2023

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.

#### 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

Credits: 5

Schedule:

Teacher in charge (valid for whole curriculum period):

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

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

CEFR level (valid for whole curriculum period):

Language of instruction and studies (applies in this implementation):

Teaching language: English. Languages of study attainment: English

#### CONTENT, ASSESSMENT AND WORKLOAD

##### Content
• valid for whole curriculum period:

- 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 for whole curriculum period:

lectures, exercises and course exam OR exam only

• valid for whole curriculum period:

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

#### DETAILS

##### Substitutes for Courses
• valid for whole curriculum period:

##### Prerequisites
• valid for whole curriculum period:

#### FURTHER INFORMATION

##### Further Information
• valid for whole curriculum period:

Teaching Language : English

Teaching Period : 2022-2023 Spring III
2023-2024 Spring III

Enrollment :

Registration takes place in Sisu (sisu.aalto.fi).