Admission requirements
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:
You will find the timetables for all courses and degree programmes of Leiden University in the tool MyTimetable (login). Any teaching activities that you have sucessfully registered for in MyStudymap will automatically be displayed in MyTimetable. Any timetables that you add manually, will be saved and automatically displayed the next time you sign in.
MyTimetable allows you to integrate your timetable with your calendar apps such as Outlook, Google Calendar, Apple Calendar and other calendar apps on your smartphone. Any timetable changes will be automatically synced with your calendar. If you wish, you can also receive an email notification of the change. You can turn notifications on in ‘Settings’ (after login).
For more information, watch the video or go the the 'help-page' in MyTimetable. Pleas note: Joint Degree students Leiden/Delft have to merge their two different timetables into one. This video explains how to do this.
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.
Reading list
- Bertsekas, Dimitri, and John N. Tsitsiklis. Introduction to probability. Vol. 1. Athena Scientific, 2008.
- Papoulis, Athanasios. Probability and statistics. Prentice-Hall, Inc., 1990.
- Ross, Sheldon M., et al. A first course in probability. Vol. 2. New York: Macmillan, 1976.
Registration
From the academic year 2022-2023 on every student has to register for courses with the new enrollment tool MyStudymap. There are two registration periods per year: registration for the fall semester opens in July and registration for the spring semester opens in December. Please see this page for more information. An exemption is the fall semester for 1st year bachelor students, the student administration will enroll this group.
Please note that it is compulsory to register for every exam and retake. Not being registered for a course means that you are not allowed to participate in the final exam of the course.
Extensive FAQ on MyStudymap can be found here.