## Some basics on probability theory

Probability theory is a branch of mathematics, and it forms the basics to infer from a sample to a population. Together with the field of analytical statistics, probability theory is used in the field of stochastic to describe random events. Stochastic modeling in turn uses probabilistic concepts—randomness and laws regarding randomness—for the modeling and analysis of real random processes (for example, in economic forecasting). Let's introduce some notation and basic concepts.

A random process or random experiment is any procedure that can be infinitely repeated and has a well-defined set of possible outcomes. For example, rolling a die is a random experiment.

The set of outcomes is denoted by . These are all possible outcomes of the random experiment. Example: for rolling a die, .

A random variable, , can take on a set of possible different values (by chance), each with an associated probability.

The output of the random experiment is a random variable. Example...