A cumulative population fraction is an ordinary function, not a random variable. It is a function which describes the distribution of a random variable.

Thanks Richard. Let´s remember that we are in a context in which data is ordered according to X variable, so p cumulated fractions are shaped by that ordering, and at the same time p fractions remain between (0;1]. I understand randomness more as a procedure to generate unbiassed values between two predefined limits rather than a property of population or of measured variables by theirselves. We use them to design the experiment population with smaller samples which we declare "representative" of the whole studied population. For this reason I ask myself and people like you if X variables are just "functions" of aleatory populations mediated by an structural relationship present in reality? If we want to study that case it is because the goal is to understand the distribution, or relation between variable and unbiassed population. This theme was partially considered in another forum question made by Hemanta Baruah about randomness that was quite visited few months ago.

Note: in the original explanation of question I made a typing error, so excuse me please. At the end, It should say:

"... we can not say here that P is aleatory, because it is dependent of prior values of X and of the relationship that links it with X. They switched rolls ....".

Thanks, emilio