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Lamun variabel acak X dibérékeun sarta distribusina kaasup kana fungsi probabiliti densiti f(x), mangka nilai ekspektasi X (lamun éta aya) bisa diitung ku

Not every probability distribution has a density function: the distributions of discrete random variables do not; nor does the Cantor distribution, even though it has no discrete component, i.e., does not assign positive probability to any individual point.

A distribution has a density function if and only if its cumulative distribution function F(x) is absolutely continuous. In this case, F is almost everywhere differentiable, and its derivative can be used as probability density. If a probability distribution admits a density, then the probability of every one-point set {a} is zero.

It is a common mistake to think of f(a) as the probability of {a}, but this is incorrect; in fact, f(a) will often be bigger than 1 - consider a random variable with a uniform distribution between 0 and 1/2.

Dua densiti f jeung g for the same distribution can only differ on a set of Lebesgue measure zero.