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Introduction Mathematical Statistics


Admission requirements

Introduction to probability theory
Analysis 1 (both not mandatory)


We learn to translate real world problems into probability models. By analyzing them with tools from probability theory, we can gain valuable information about the original problem. In this course we focus on models which depend on a finite number of parameters. We learn two general principles to estimate these parameters: the method of moments and the maximum likelihood principle. Nearly as important as fitting the model is to quantify the uncertainty of our estimation. This leads to the concept of confidence intervals. To draw conclusions with high confidence, we introduce hypothesis tests.

Course Objectives

After the course the students are able to translate real world problems into simple parametric models. Respective parameters can be fitted by either maximum likelihood estimation or moment estimators. Students can quantify the uncertainty of the estimations by bias, variance and confidence intervals. By constructing hypothesis tests, conclusions can be drawn with a high confidence. Students are aware of the necessary simplifying assumptions to translate a problem into a managable probabilistic model and know tools to check them. After the course, students will have basic knowledge of the statistical software R.


The schedule for the course can be found on MyTimeTable.

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. Please note: Joint Degree students Leiden/Delft have to merge their two different

Mode of instruction

Lectures tutorials and homework

Assessment method

The final grade consists of homework (20%) and a written (retake) exam (80%). To pass the course, the grade for the (retake) exam should be at least 5 and the (unrounded) weighted average of the two partial grades at least 5.5. No minimum grade is required for the homework in order to take the exam or to pass the course. The homework counts as a practical and there is no retake for it.

Reading list

Fetsje Bijma, Marianne Jonker, Aad van der Vaart: An Introduction to Mathematical Statistics. Amsterdam University Press 2017.


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.

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.


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