A probability density function (PDF) is a statistical function that describes the likelihood of a continuous random variable taking on a specific value. Unlike discrete probabilities, which assign probabilities to distinct outcomes, a PDF provides a curve where the area under the curve represents the probability of the variable falling within a certain range. The total area under the PDF curve equals 1, indicating that the variable will take on some value within its range. In mathematical terms, the PDF is often denoted as f(x) for a random variable X. To find the probability that X falls between two values, you would calculate the area under the curve of f(x) between those two points. This concept is fundamental in fields such as statistics, data analysis, and machine learning.