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.