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Statistics and probability


Admission Requirements



The first half of this course is an introduction to probability theory. We start with the definition of a probability distribution, and discuss conditional probabilities and (conditional) independence. Next, we introduce a number of well known and much used probability distributions and consider joint distributions of multiple, dependent variables. We define the expectation, variance and covariance and finally we discuss two important Theorems: the Law of Large Numbers and the Central Limit Theorem.

The second half of the course is an introduction to statistics. On the basis of data we try to draw conclusions about the (random) process that generated those data. We discuss estimation theory where we attempt to find the probability distribution that “"best" fits the data. In particular, we consider the method of maximum likelihood. Next, we look at testing hypotheses, where we try to determine if the data are consistent with some hypothesis, or not.

Course objectives

Obtain introductory knowledge of Probability Theory and Statistics.


See the Leiden University students' website for the Statistics and Data Science programme.

Mode of Instruction

Lectures, problem sessions, self study.

Assessment method

There are two partial exams. The homework does not contribute to the final grade.

Reading list

Recommended: Mathematical Statistics and Data Analysis. John A. Rice, Duxbury press (3-rd ed. 2007)


Enroll in Usis for the course materials and course updates.

To be able to obtain a grade and the EC for the course, sign up for the (re-)exam in uSis ten calendar days before the actual (re-)exam will take place. Note, the student is expected to participate actively in all activities of the program and therefore uses and registers for the first exam opportunity.

Make sure you use the codes provided:
General Lecture: 4433STPRBH
Exam Statistics: 4433STPRST
Exam Probability: 4433STPRBT