What conditions must a probability density function satisfy?

In the study of probability and statistics, a probability density function (PDF) is a function used to describe the distribution of a continuous random variable. To be considered a valid probability density function, the function $f(x)$ must satisfy the following two conditions:

• Non-negativity: The function must be nonnegative for every value of the random variable; that is, $f(x)\ge 0$ for all $x$.1
• Normalization: The total area under the graph of the function must equal one. Mathematically, this means the integral of the function over all possible values of the random variable must equal one: ${\int }_{-\infty }^{\infty }f(x)dx=1$.21

While the PDF does not directly provide the probability of the variable taking on a specific value, the probability that the variable falls within a particular interval is determined by calculating the integral of the function over that interval.21