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The Magic Cafe Forum Index » » Puzzle me this... » » 2 points on a sphere (0 Likes) Printer Friendly Version

Nir Dahan
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Inner circle
Munich, Germany
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Two points on the surface of a sphere are drawn uniformly at random. What is the maximum likelihood estimate of the distance between these two points?
magicgeorge
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Belfast
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Hello,
What is a 'maximum likelihood estimate"?

The maximum distance is 2r

The average would be somewhere between 0 and 2 r.

If the maximum likelihood means the most likely distance then I assume it's the most common distance.

I think this might be the root of 2 times r because the most common distance will be from the beginning spot to the longest perimetre on which it can finish which would be 90 degrees around the ball from the starting point, hence the distance would be the hypotenuese of a triangle with two sides of r.

George
Nir Dahan
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Inner circle
Munich, Germany
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Again correct
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