Fungsi dénsitas probabilitas: Béda antarrépisi
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Dina [[matematika]], '''probability density function'''
Formally, a probability distribution has density ''f''(''x'') if ''f''(''x'') is a non-negative [[Lebesgue integration|Lebesgue-integrable]] function '''R''' → '''R''' such that the probability of the interval [''a'', ''b''] is given by
:<math>\int_a^b f(x)\,dx</math>
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:<math>f(x)={e^{-{x^2/2}}\over \sqrt{2\pi}}</math>.
Lamun [[variabel acak]] ''X''
:<math>\operatorname{E}(X)=\int_{-\infty}^\infty x\,f(x)\,dx</math>
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Not every probability distribution has a density function: the distributions of [[discrete random variable]]s 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 [[absolute continuity|absolutely continuous]]. In this case, ''F'' is [[almost everywhere]] [[derivative|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 [[sebaran seragam|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.
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