2Probabilistic Models
CONCEPTS DISCUSSED IN THIS CHAPTER.– We will begin by looking at the concept of random variables. For concrete mathematical processing, it is convenient to make a variable correspond to the occurrence of a random event. Hence, it is called a “random variable”. This random variable can take discrete values or continuous values.
We will then review some common probability laws. Probability laws are functions of a random variable. We will show their main characteristics.
Finally, at the end of the chapter, we discuss stochastic processes: their definition in terms of the family of random variables according to the same probability law and their categorization.
Recommended reading: [BRE 09, PHE 77, SAP 11].
2.1. Random variables
In an experiment, we make an inventory of the results which can occur, i.e. possible events: A, B, C,..., K. We correspond the values of a variable X to these events:
- – for the event A, X = 1;
- – for the event B, X = 2;
- – for the event C, X = 3;
- – ...;
- – for the event K, X = n.
Such a variable, associated with a set of possible events, is called a random variable. The definition, for any value of X, of the corresponding probability is a law of probability.
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