Béda révisi "Fungsi dénsitas probabilitas"

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Dina [[matematika]], '''probability density function''' dipakedipaké keur ngagambarkeun [[probability distribution]] di watesan [[integral]]s. Lamun probability distribution ngabogaan densiti ''f''(''x''), saterusna [[interval (mathematics)|interval]] tak terhingga [''x'', ''x'' + d''x''] ngabogaan probabiliti ''f''(''x'') d''x''. Probability density function bisa ogeogé ditempo tina versi "smoothed out" [[histogram]]: if one empirically measuresméasures values of a [[variabel acak]] repeatedlyrepéatedly 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 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>
:<math>f(x)={e^{-{x^2/2}}\over \sqrt{2\pi}}</math>.
Lamun [[variabel acak]] ''X'' diberekeundibérékeun sarta distribusina kaasup kana fungsi probabiliti densiti ''f''(''x''), mangka [[nilai ekspektasi]] ''X'' (lamun etaéta aya) bisa diitung ku
:<math>\operatorname{E}(X)=\int_{-\infty}^\infty x\,f(x)\,dx</math>
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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