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 random variables, where probabilities can be assigned directly, a PDF provides a density value that must be integrated over an interval to yield a probability. The area under the curve of a PDF across a range of values represents the probability of the variable falling within that range. Common examples of PDFs include the normal distribution and the exponential distribution, each characterized by specific mathematical formulas that define their shapes and behaviors.