The significance of the pdf is that is the probability that the r.v. is in the interval , written as:
This is an operational definition of . Since is unitless (it is a probability), then has units of inverse r.v. units, e.g., 1/cm or 1/s or 1/cm, depending on the units of x. Figure 4 shows a typical pdf and illustrates the interpretation of the probability of finding the r.v. in with the area under the curve from x to x+dx.
We can also determine the probability of finding the r.v. somewhere in the finite interval :
which, of course, is the area under the curve from x=a to x=b.
Figure 4: Typical Probability Distribution Function (pdf).