In article <email@example.com>, tony richards <firstname.lastname@example.org> wrote:
> I make that a fraction 0.834 (or 0.849 for the earlier run) for obtuseness.
I got 0.833 from 10 million trials (if I remember the last digit correctly), so you are correct.
> SO where is the 0.75 answer everyone else expects?
Who says everyone expects 0.75. The answer 0.75 is specific to certain distributions only. Surprisingly, several different approaches lead to the same answer, but that's no reason to believe that the Cauchy will give this answer. The point about the Cauchy is that it has a long tail. It is therefore not unlikley that two vertices will be moderately far into the tails while one is near the middle, and this is more likely to give an obtuse angle at the more central point.
> Don't tell B.Taylor - he'll just call you a wally or > worse.
No, he'll call someone who expects the answer to be 0.75 a wally, and quite rightly IMO.
Terry Moore, Statistics Department, Massey University, New Zealand.
Theorems! I need theorems. Give me the theorems and I shall find the proofs easily enough. Bernard Riemann