can you explain?

Definition 3.3 Probability Mass Function (PMF) The probability mass function (PMF) of the discrete random variable X is af Pes) HP LX Sa] Note that X = x is an event consisting of all outcomes s of the underlying exper- iment for which X(s) = x. On the other hand, Px(z) is a function ranging over all real numbers 2. For any value of , the function Px(a) is the probability of the event X = 2. Observe our notation for a random variable and its PMF. We use an uppercase letter (X in the preceding definition) for the name of a random variable. We usually use the corresponding lowercase letter (2) to denote a possible value of the random variable. The notation for the PMF is the letter P with a subscript indicating the name of the random variable. Thus Ppr(r) is the notation for the PMF of random variable R. In these examples, r and 2 are dummy variables. The same random variables and PMFs could be denoted Ppr(w) and Px(u) or, indeed, Pp(-) and Px(-). We derive the PMF from the sample space, the probability model, and the rule that maps outcomes to values of the random variable. We then graph a PMF by marking on the horizontal axis each value with nonzero probability and drawing a vertical bar with length proportional to the probability