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numana Heavyside [[step function]] θ(''x'') ngarupakeun CDF tina degenerate sebaran dina ''x'' = 0.
== TheKasus continuous casekontinyu ==
Dina kasus kontinyu, sebaran seragam disebut oge '''sebaran bujursangkar''' sabab bentuk tina fungsi densiti probabiliti (tempo di handap). Hal ieu di-parameterisasi ku nilai pangleutikna jeung panggedena tina kaseragaman-sebaran [[random variable]] nu dicokot nyaeta ''a'' jeung
In the continuous case, the uniform distribution is also called the '''rectangular distribution''' because of the shape of its probability density function (see below). It is parameterised by the smallest and largest
''b''. [[Probability density function]] sebaran seragam nyaeta:
values that the uniformly-distributed [[random variable]] can take, ''a'' and
''b''. The [[probability density function]] of the uniform distribution is thus:
:<math>
</math>
and thesarta [[cumulative distribution function]] isnyaeta:
:<math>
</math>
Grapik pungsi densiti probabiliti keur sebaran seragam siga di handap ieu:
The graph of the probability density function for the continuous uniform distribution looks like:
[[image:uniform_pdf.png|center|314px]]
<center>'''ThePungsi continuousdensiti uniformprobabiliti probabilitytina densitysebaran functionseragam kontinyu'''</center>
For aKeur [[random variable]] followingnu thisnuturkeun distributionsebarn ieu, the [[expected value]] isnyaeta (a + b)/2 and thesarta [[standardsimpangan deviationbaku]] isnyaeta
(b - a)/√12.
ThisSebaran distributionieu canbisa bedipake generalizedkeur tosusunan morenu complicatedleuwih setskompleks thantinimbang intervalsinterval. IfLamun ''S'' isngarupakeun asusunan Borel set of positivepositip, finiteukuran measure''terhingga'', thesebaran uniformprobabiliti probabilityseragam distribution ondina ''S'' canbisa bedihusukeun specifiedku bynyebutkeun saying that theyen pdf isnyaeta zeronol outsidediluar ''S'' andsarta constantlysacara equalangger tosarua jeung 1/''K'' ondina ''S'', wherenumana ''K'' is theukuran Lebesgue measure oftina ''S''.
=== The standard uniform distribution ===
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