A.15 Uniform distribution
X has a uniform distribution on the interval (a, b) denoted
if it has density
where
is the indicator function of the set (a, b). The mean and variance are
There is no unique mode, but the distribution is symmetrical, and hence
Sometimes we have occasion to refer to a discrete version; Y has a discrete uniform distribution on the interval [a, b] denoted
if it has a discrete distribution with density
The mean and variance are
using formulae for the sum and sum of squares of the first n natural numbers [the variance is best found by noting that the variance of UD(a, b) equals that of UD(1, n) where n=b–a+1]. Again, there is no unique mode, but the distribution is ...
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