What does the lower case "r" represent in this definition of random variable? Also, what is the conventional way to read that entire pink box?So far I read it as follows: "random variable 'X' such that (:) the sample space (omega) maps to a real number (R) such that for all (upsideown A) "r" is an element (E) of the real numbers (R), { state of the world (w) is an element (E) of the sample space (omega) such that (:) random variable 'X' is less than or equal to 'r'} (E) S. I know I totally got the that wrong lol

a quantity that has yet to be determined by a random generative process, just as ordinary algebraic variables represent unknown or unspecified quantities. However, the technical definition of a random variable is less intuitive and requires some careful discussion. Formally, a random variable is a real-valued function of the outcome of a random generative process. Definition 1.2.1. Random Variable A random variable is a function X : 0 - R such that, Vr ER, (W En : X ( W)