Probability Theory - Period 4+5

We study experiments in which randomness plays a role. We first consider discrete probability experiments, that is experiments with a countable number of possible outcomes. You can think of tossing dice, shuffling a deck of cards, flipping coins etc. The possible outcomes form a set, the so called sample space. Every subset of this sample space is an event. We assign probabilities to events in a reasonable way, such that the three axioms of probability are satisfied. We compute probabilities in these situations and consider associated concepts like independence, conditional probabilities, random variables and important discrete probability distributions like the Bernoulli, Binomial, geometric, hypergeometric, negative Binomial and Poisson distribution.

We then consider experiments with an uncountable number of possible outcomes and continuous random variables. We treat a number of well-known continuous distributions: the uniform, exponential, normal and exponential distributions. We study joint distributions of several (discrete or continuous) random variables. In this context we treat independence, conditional distributions and expectations, distributions and expectations of functions of random vectors and covariance. We study the Central limit theorem and the normal approximation to the Binomial distribution.

Contact hours listed under a course description may vary due to the combination of lecture-based and independent work required for each course therefore, CEA's recommended credits are based on the ECTS credits assigned by VU Amsterdam. 1 ECTS equals 28 contact hours assigned by VU Amsterdam.