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).