# Probability Theory for Computer Scientists

Course
2024-2025

## Description

In this class, students will learn how to model, quantify, and analyze uncertainty. The fundamental tools of probability will be covered which are essential to analyze and make sense of data. The course will focus on introducing basic concepts and methodologies, and will contain multiple examples and real-world applications.

In the course, we cover the following topics:

• Axioms of probability

• Probability mass/distribution functions

• Expectation, variance, and covariance

• Conditional probability

• Independence, Conditional Independence

• Bayes’ Rule, Bayesian inference

• Law of large number

## Course objectives

At the end of the course, the student is able to:

• translate probability queries described in words to mathematical ones.

• explain common probability distributions (such as Bernoulli, Gaussian, Exponential,… distributions).

• calculate probability mass functions, densities, conditional probabilities, and expectations.

• explain the concepts of laws of large numbers, independence, and conditional independence.

• derive indepedence and conditional indepedence.

• explain the main concept and assumptions underlying Bayesian inference.

## Timetable

The most updated version of the timetables can be found on the students' website:

In MyTimetable, you can find all course and programme schedules, allowing you to create your personal timetable. Activities for which you have enrolled via MyStudyMap will automatically appear in your timetable.

Questions? Watch the video, read the instructions, or contact the ISSC helpdesk.

Note: Joint Degree students from Leiden/Delft need to combine information from both the Leiden and Delft MyTimetables to see a complete schedule. This video explains how to do it.

## Mode of instruction

For four weeks, 4 hours of lecture and for two weeks, 2 hours of lecture and 2 hours of working group.

## Assessment method

There are an ANS exam and three assignments. The assignments can be completed and submitted during the semester according to the deadlines.

The weighting of the final grade will be:

• 70% Final exam

• 30% The average grade of the three assignments

Students can use any material in submitting the assignments but they are responsible for the entire content of the assignment. Students may be randomly selected to discuss the approach they used in their assignments. It is allowed to retake the final exam (not the assignments) if a student cannot pass the final exam.

1. Bertsekas, Dimitri, and John N. Tsitsiklis. Introduction to probability. Vol. 1. Athena Scientific, 2008.
2. Papoulis, Athanasios. Probability and statistics. Prentice-Hall, Inc., 1990.
3. Ross, Sheldon M., et al. A first course in probability. Vol. 2. New York: Macmillan, 1976.

## Registration

As a student, you are responsible for enrolling on time through MyStudyMap.

In this short video, you can see step-by-step how to enrol for courses in MyStudyMap.
Extensive information about the operation of MyStudyMap can be found here.

There are two enrolment periods per year:

• Enrolment for the fall opens in July

• Enrolment for the spring opens in December

Note:

• It is mandatory to enrol for all activities of a course that you are going to follow.

• Your enrolment is only complete when you submit your course planning in the ‘Ready for enrolment’ tab by clicking ‘Send’.

• Not being enrolled for an exam/resit means that you are not allowed to participate in the exam/resit.

## Remarks

Software
Starting from the 2024/2025 academic year, the Faculty of Science will use the software distribution platform Academic Software. Through this platform, you can access the software needed for specific courses in your studies. For some software, your laptop must meet certain system requirements, which will be specified with the software. It is important to install the software before the start of the course. More information about the laptop requirements can be found on the student website.