This is from Feller (vol. II), not exactly a high school text. Definition 3. A random variable X is a real function which is measurable with respect to the u

This is from Feller (vol. II), not exactly a high school text. Definition 3. A random variable X is a real function which is measurable with respect to the underlying sigma-algebra. The function F defined by F(T) = P{X < T} us called the distribution function of X. (He introduces later complex-valued random variables though - in the context of characteristic functions.)