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A common distribution for discrete and continuous properties is the uniform distribution on a given interval. According to a uniform distribution, a random variable is equally likely to take any value in the assigned interval. Hence, the PDF is constant within the interval, and 0 elsewhere. If a random variable X is distributed according to a uniform distribution U([a, b]) in the interval [a, b], then its PDF f_X(x) can be written as:

(1.30)

The mean μ_X of a uniform distribution in the interval [a, b] is:

(1.31)

and it coincides with the median, whereas the variance is:

(1.32)

An example of uniform distribution in the interval [1, 3] is shown in Figure 1.7. The uniform distribution is sometimes called non‐informative because it does not provide any additional knowledge other than the interval boundaries.