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.
Obtain introductory knowledge on Probability Theory and Statistics.
For the course days, course location and class hours check the Time Table 2013-14 under the tab “Masters Programme” at http://www.math.leidenuniv.nl/statscience
Mode of Instruction
This course is a combination of lectures, problem sessions and computer practicals.
Two written exams, each account for 50% of the grade.
The written exam, for the first part of the course, is scheduled for 25 September 2013 from 14.00 to 16.00 hours. For the second part of the course a written exam is planned on the 4th of November 2013 from 14.00 to 16.00 hours.
The resits for both exams are scheduled for 31 January 2014 at 10.00-12.00 (Intro Probability) and 14.00 – 16.00 (Intro Stat).
Mathematical Statistics and Data Analysis. John A. Rice, Duxbury press (3-rd ed. 2007)
E.W.van_Zwet [at] lumc [dot] nl
- This is a compulsory course in the Master’s programme of the specialisation Statistical Science for the Life & Behavioural sciences.