The chance that a continuous random variable is in any range of values can be calculated as the area under a curve over that range of values. The curve is the probability density function of the random variable. That is, if X is a continuous random variable, there is a function f(x) such that for every pair of numbers a≤b,

P(a≤ X ≤b) = (area under f between a and b);

f is the probability density function of X. For example, the probability density function of a random variable with a standard normal distribution is the normal curve. Only continuous random variables have probability density functions.