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Dina matematika, probability density function dipaké keur ngagambarkeun probability distribution di watesan integrals. Lamun probability distribution mibanda densiti f(x), saterusna interval tak terhingga [x, x + dx] mibanda probabiliti f(x) dx. Probability density function bisa ogé ditempo tina versi "smoothed out" histogram: if one empirically méasures values of a variabel acak repéatedly and produces a histogram depicting relative frequencies of output ranges, then this histogram will resemble the random variable's probability density (assuming that the variable is sampled sufficiently often and the output ranges are sufficiently narrow).

Formally, a probability distribution has density f(x) if f(x) is a non-negative Lebesgue-integrable function R → R such that the probability of the interval [a, b] is given by

for any two numbers a and b. This implies that the total integral of f must be 1. Conversely, any non-negative Lebesgue-integrable function with total integral 1 is the probability density of a suitably defined probability distribution.

Contona, sebaran seragam dina interval [0,1] mibanda probabiliti densiti f(x) = 1 keur 0 ≤ x ≤ 1 jeung nol dimamana. Standar sebaran normal mibanda probabiliti densiti