AAWSAP DIRD, An Introduction to the Statistical Drake Equation, March 2010

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and finally

$$
p(x) = \frac{1}{b_i - a_i} \quad \text{with} \quad a_i \le x \le b_i
$$

showing that the maximum-entropy probability distribution over any FINITE interval $a_i \le x \le b_i$ is the UNIFORM distribution.

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