ABSTRACT
Section 13.3 introduced the concept of the relation between two different ways of partitioning the sample space. Given two random variables, X and Y , we could use the values of X and the values of Y to partition S, then use the methods of Section 13.3 to determine if there is compelling evidence against the null hypothesis that X and Y are independent. However, if X and Y have many possible values, then using these values to define small numbers of cells results in a fairly crude approximation of the relation between X and Y . Furthermore, this relation does not exploit various useful properties of real numbers, e.g., that x1, . . . , xr can be meaningfully ordered from smallest to largest.
