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probability density function (pdf)

In probability theory, a probability density function (pdf), or density of a continuous random variable is a function that describes the relative likelihood for this random variable to occur at a given point. The probability for the random variable to fall within a particular region is given by the integral of this variable’s density over the region. The probability density function is nonnegative everywhere, and its integral over the entire space is equal to one.

Intuitively, one can think of f(x) dx as being the probability of X falling within the infinitesimal interval [x, x + dx].

If a random variable X is given and its distribution admits a probability density function f, then the expected value of X (if it exists) can be calculated as

    \operatorname{E}[X] = \int_{-\infty}^\infty x\,f(x)\,dx.



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