can you explain?

Definition 3.2 Discrete Random Variable X is a discrete random variable if the range of X is a countable set Sx = {x1, x2, ...}. The defining characteristic of a discrete random variable is that the set of possible values can (in principle) be listed, even though the list may be infinitely long. Often, but not always, a discrete random variable takes on integer values. An exception is the random variable related to your probability grade. The experiment is to take this course and observe your grade. At Rutgers, the sample space is S = { F, D. C. C+, B, B+, A ) . (3.5) We use a function Gi(.) to map this sample space into a random variable. For example, G1(A) = 4 and G1(F) = 0. The table Outcomes F D C C+ B B+ A G1 0 1 2 2.5 3 3.5 4