o the true analogy is not between a density function fX (x) and a mass function pY (x) but instead between fX (x)x and pY

o the true analogy is not between a density function fX (x) and a mass function pY (x) but instead between fX (x)δx and pY (x). This is borne out by comparing (5.25) with (2.6): values of the mass function are replaced by fX (x)δx, and the summation (since, for discrete random variables, only countably many values are positive) is replaced by the integral. A startling difference between discrete and continuous random variables is given in the first part of the next theorem.