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# Notion of Probability

Whether it is experiments carried out in reverberation chambers or theoretical simulations of these tools, the data such as the electric field or the power collected in the room behave like random variables. The developments related in Chapter 3 frequently use the main results of the theory of probabilities. Some notions about this theory will be recalled in this appendix [BAS 67].

# A1.1. The random variable concept

A random variable is represented by a number, whose quite unpredictable behavior can be attached to a probability distribution. In the context of the book, the random variables will follow a continuous description. These variables, often denoted by a small letter, will belong to the set of real numbers. However, their domain can be bounded and restricted in the positive real numbers or extended to all real numbers, as illustrated below:

[A1.1]

# A1.2. Probability concept from intuition

Let us consider an experiment, whose aim is to take a variable x staggered on N discrete values, which are defined by the following conventions:

[A1.2]

During tN experiments, the Xi value appears ti times. An estimate of the Pi probability, of instance Xi, will thus be given by the ti/tN ratio, i.e.:

[A1.3]

Intuitively, we realize that by indefinitely increasing ...

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