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1 Introduction

This paper examines the pertinence of using the \( \chi ^{2}\, law\) to model the behavior of the \( Pearson's\, \chi ^{2}\) statistic. Therefore sec: chichi_chilaw is devoted to recall some definitions and properties of both concepts, and emphasise their differences. Several proofs are given in the annexes A.1.

Thereafter, these notions will be applied, in sec: lowbrow level and sec: fair dice, to the simulation of, respectively, an unfair and a fair die. The reader is requested to be patient with the unfair die section : the aim is not another undergraduate exposition, but to allow a comparison with the fair die case, where all these well known things cease to be relevant. A conclusive section and a bibliography are supplied.


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douillet@ensait.fr
2002-10-01