Probability Theory

Probability theory comprises mathematically based theories and methods for investigating random phenomena. Formally, random phenomena occur in connection with random experiments. A random experiment is characterized by two properties: 1. Repetitions of the experiment, even if carried out under identical conditions, generally have different outcomes. 2. The possible outcomes of the experiment are known. Thus, the outcomes of a random experiment cannot be predicted with certainty. However, if random experiments are repeated sufficiently frequently under identical conditions, stochastic or statistical regularities can be found. Examples of random experiments are: 1) Counting the number of vehicles arriving at a filling station a day. 2) Counting the number of shooting stars during a fixed time interval. The possible outcomes are, as in the previous random experiment, nonnegative integers. 3) Recording the daily maximum wind velocity at a fixed location. 4) Recording the lifespans of technical systems or organisms. 5) Recording the daily maximum fluctuation of share prices. The possible outcomes are, as in the random experiments 3 and 4, nonnegative numbers. 6) The total profit sombody makes with his financial investments a year. This 'profit' can be negative, i.e. any real number can be the outcome. As the examples show, in this context the term 'experiment' has a more abstract meaning than in the customary sense.