Admission Requirements

Description
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 on Probability Theory and Statistics.
Time Table
For the course days, course location and class hours check the Time Table under the
tab “Statsci Students —> Program Schedule” at <http://www.math.leidenuniv.nl/statscience>
Mode of Instruction
This course is a combination of lectures, problem sessions and computer practicals.
Assessment method
Two written exams, one for the Probability part and one for the Statistics part, each accounts for 50% of the grade.
Date information about the exam and resit can be found in the Time Table pdf document under the tab “Masters Programme” at <http://www.math.leidenuniv.nl/statscience>. The room and building for the exam will be announced on the electronic billboard, to be found at the opposite of the entrance, the content can also be viewed here.
Reading list
Mathematical Statistics and Data Analysis. John A. Rice, Duxbury press (3rd ed. 2007)
Registration
Enroll in Blackboard for the course materials and course updates.
To be able to obtain a grade and the ECTS 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.
Contact information
E.W.van_Zwet [at] lumc [dot] nl
Remarks
 This is a compulsory course in the Master’s programme of the specialisation Statistical Science for the Life & Behavioural sciences.