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AllanCrossman comments on A Request for Open Problems - Less Wrong
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Well. So if all men were within 10 cm of each other, and uniformly distributed, and we plucked 2 random men out, and they were 4cm apart, would c be between them with 80% probability? Or some other value?
The shorter man can be between c-5 and c+1 with all values equally probable, if he's between c-5 and c-4 or c and c+1 then c is not between them, if he's between c-4 and c then c is between them, so assuming a uniform prior for c the probability is 2/3 if I'm not mistaken.
Ah, I see what I did wrong. I think.
Yup. Under the uniform prior the posterior probability that c is between the two values is d/(1 - d), 0 < d < 0.5, where d = x_max - x_min (and the width of the uniform data distribution is 1).
The answer to that depends on what you know about c beforehand -- your prior probability for c.