3. Probability calculus

3.1 Probability spaces and random variables

In most cases, it is impossible to carry out an exhaustive measurement, verification or experiment on an entire collection of objects (or people), and this leads to the selection of significant samples on which to work. This natural approach immediately poses two problems: how to obtain the sample? How large does it have to be to be significant?

To eliminate any arbitrary choice on the part of the experimenter, sample elements should be chosen "at random". As for the sample size, this should enable us to obtain a result that is "probably" accurate to within a "small error".

To replace the expressions in quotation marks above with precise notions and quantitative data, we need a mathematical...