657. Why, when testing the hypothesis of a uniform distribution of the population $X$ using the Pearson's criterion, is the number of degrees of freedom determined by the equation $k=s-3$, where $s$ is the number of intervals in the sample?
Solution. When using the Pearson criterion, the number of degrees of freedom $k=s-1-r$, where $r$ is the number of parameters estimated from the sample. The uniform distribution is defined by two parameters $a$ and $b$. Since these two parameters are estimated from the sample, $r=2$, and therefore, the number of degrees of freedom $k=s-1-2=s-3$.