Interconnections between the theory of probability and the statistics
Although confusion is often made, the Theory of probability and the Statistiques are two branches distinct from mathematics. The theory of probability is the mathematical study of the phenomena characterized by the chance and uncertainty, whereas the statistics are the activity which consists to collect, treat and interpret a whole of data.
The bond between the two comes owing to the fact that when a statistical whole of data is studied, a particularly important method consists in supposing that these data are the realization of a Random variable . One places oneself then within the framework of the Statistique mathematics. One thus calls upon the theory of probability to include/understand statistics. Also when one checks by a statistical series representative a function of transfer of the type Y=F (x1) +F (x2) +F (Xn)…. it is possible to calculate the probabilities of Y according to the possible occurrences of variables Xi.
Conversely when a random phenomenon is studied, one is often interested in the statistics generated by one or more pulling of this random variable. The Loi of the great numbers guarantees that in a series of big size, more one increases the sample size, more the statistical characteristics of the sample approach the characteristics of the random variable.
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