# Probability and Statistics

 Credits 6 credit points Instructors Tijms, H.C. (Vrije Universiteit) E-mail h.c.tijms@vu.nl Aim The aim of this course is to familiarize future teachers with the basic concepts and ideas of probability theory and statistics and to demonstrate the relevance of these subjects for science and society. Description Probability theory is a subject that even the most mathematically competent often find difficult to use and understand. There are no complicated rules to learn,  but many of the students find the ideas of probability difficult to grasp. In the field of probability it is not possible to proceed by memorizing worked solutions to standard  problems, but creative thinking is required all the time.  In this course the concepts of probability will be taught through the use of motivating and insightful examples and problems. In interaction with theory, simulation will be used to clarify the basic concepts of probability. Also, time will be made for self-activity during the classes by solving probability problems in teamwork. The student learns most by practicing with a lot of problems to really understand what the subject is about.Next to  the treatment of standard topics from a first course in probability, such as discrete and continuous random variables, expected value, probability distribution function, probability density, etc., special attention is given to(a)  Poisson approximations with applications(b)  The law of large numbers and Kelly betting(c)   Random-number generators and simulating from probability distributions(d)  Geometric probability(e)  The central limit theorem and statistical applications(f)   Conditional probabilities and Bayesian inference.If  time permits and depending on the interests of the  participants, related topics can be added such as absorbing Markov chains for success runs and stochastic optimization in stopping problems. Organization Lectures integrated with self-activity in the class. Examination Written exam and take-home projects. Take-home projects will have a  strict deadline and in  the final mark they count with a  weight factor of 0.4. The take-home exams are compulsory for participation in the final written exam on January 13, 2012. Literature Henk Tijms, Understanding Probability, 2nd edition, Cambridge University Press, 2007, approx. 34 euro. Having the book is essential for the course. Prerequisites Calculus and preferably experience with a programming tool such as Matlab or Excel. Remarks The participants are strongly advised to read the Sections 2.1-2.3 and the Appendix of the mandatory textbook before the first class starts. The textbook is well suited for self-study. The participants will be asked  for each  meeting to read on beforehand the material to be discussed at  this meeting in order to improve interaction with the participants and to have more time for  jointly making and discussing exercises.
Last changed: 15-11-2013 17:02