What does a probability density function (pdf) represent?

A probability density function (pdf) represents the probability that a continuous random variable will fall within a specified range of values. This concept is fundamental in the context of continuous random variables, which can take on any value within a given interval. Unlike discrete random variables, which have specific probabilities assigned to each possible outcome, continuous random variables require a different approach since there are infinitely many possible values.

The pdf provides a way to describe the relative likelihood of these values by giving the density of probabilities at each point in the continuous space. To find the probability that the random variable falls within a certain range, one must calculate the area under the curve of the pdf over that interval. This area reflects the total probability of the random variable falling between those two points.

In contrast, other options refer to concepts that either apply to discrete variables, general outcomes, or total probabilities, none of which accurately describe the specific role of a pdf in relation to continuous random variables.