This is a really basic point that I am getting held up on. In probability theory, we use PDFs and PMFs to describe random variables. (The term "random variable" carries a certain connotation of "unpredictable variations when repeated.") For example, the number of heads we will see in 50 flips of a coin is a random variable. This number will change from one set of 50 flips to the next. And the changes cannot be predicted beforehand. The random variable could be described by a Bin(50, p) PMF. We could even set p = 0.5 if the coin was fair. But in statistics, PDFs and PMFs still seem to be used, to describe any quantity that we do not know for sure --- even when there isn't a scope of repetition associated with that quantity, i.e. the quantity has a real, fixed, unchanging value, just presently unknown to us. This is what is confusing me: If someone looks at a building and says that its height in feet is described by N(100, 50), and another claims that its height is described by Unif(0, 200), what are they saying exactly? The building's height is an absolute, fixed, unchanging number. What meaning does a PDF possibly have in this context?