A uniform distribution represents a belief that every possible outcome is equally likely. For a target hidden among 100 list positions, each position receives probability 1%, providing an unbiased prior before any inspection. section 6.1.3
For this finite distribution, entropy measures the remaining uncertainty: H = −Σᵢ pᵢ log pᵢ, which is roughly 6.64 when all 100 positions are equally likely. Observations update this prior into a posterior distribution. section 6.1.3
Searching a sorted list
Before searching for target z, assign every location equal probability. Inspecting one position leaves a 1% chance that z is there and a 99% chance that it is elsewhere; inspecting the middle position minimizes expected posterior entropy and motivates binary search. section 6.1.3
Figure 6.6 Prior distribution of the location of the target z within the 100-element list. Since each location is as equally likely as any other, the probability that a given location contains z is 1%.
Visualizes the uniform prior over the 100 possible target locations, with each location assigned 1%. section 6.1.3
