numana Heavyside [[step function]] θ(''x'') ngarupakeun CDF tina degenerate sebaran dina ''x'' = 0.
The continuous case ==
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
values that the uniformly-distributed [[random variable]] can take, ''a'' and
''b''. The [[probability density function]] of the uniform distribution is thus:
and the [[cumulative distribution function]] is:
The graph of the probability density function for the continuous uniform distribution looks like:
The continuous uniform probability density function'''</center>
For a [[random variable]] following this distribution, the [[expected value]] is (a + b)/2 and the [[ standard deviation]] is
(b - a)/√12.
This distribution can be generalized to more complicated sets than intervals. If ''S'' is a Borel set of positive, finite measure, the uniform probability distribution on ''S'' can be specified by saying that the pdf is zero outside ''S'' and constantly equal to 1/''K'' on ''S'', where ''K'' is the Lebesgue measure of ''S''.
=== The standard uniform distribution ===