Final answer:
The continuous curve used to describe the distribution of a continuous random variable is called the probability density function (pdf), and it graphically represents probability as the area under the curve.
Step-by-step explanation:
When discussing continuous random variables and their distributions, we describe the distribution with a curve known as the probability density function (pdf). This continuous curve represents the density of probabilities rather than the probability of individual outcomes, which is appropriate for discrete variables. In the context of a continuous random variable, this pdf curve is denoted as f(x), and it has very specific properties. For one, the area under the curve represents the probability, and for the entire range of the random variable, this area sums up to one. The curve itself must lie above the horizontal axis since probabilities cannot be negative.
Moreover, the probability of the variable falling between two points is determined by the area under the pdf curve between those points. This fundamentally distinguishes it from discrete probability distributions, which sum up individual probabilities of specific outcomes. A familiar example of a pdf is the bell-shaped curve of the normal distribution, an important probability distribution used across various disciplines.