Basics of Probabilistic Analysis for the APC-Lecture

I assume that you have some preknowledge in probability theory, but let us recapitulate the small subset of it which we will need for our purposes. We will employ very concrete probability theory (as opposed to abstract probability theory); we simply use it as a tool. When writing this I borrowed much from Chapter 8 in the book Concrete Mathematics, A Foundation for Computer Science by Ronald L. Graham, Donald E. Knuth and Oren Patashnik (Addison-Wesley (1989)). A book to be recommended not only for that chapter. We restrict ourselves to discrete probability spaces, and we will omit `discrete' from now on. Roughly speaking, such a probability space consists of a (possibly innite) set of things that can happen, each of which gets assigned a probability that it happens. This mapping is called probability distribution, since it distributes the value 1 among the things that can happen.