There is an eastwest street of length L units. And we park cars of unit length along the north side until we can't place any more cars. Each car is placed randomly (uniformly).
What is the expected number of cars that can be parked (as a function of L)?
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I'll start you off...
For 0 <= L < 1, F(L) = 0
For 1 <= L < 2, F(L) = 1
Okay... now the easy ones are out of the way, can you describe the function for L>=2?
I would think that for 2.1 it would be unlikely to park 2 cars. For 2.9, it would be hard to park only 2 cars. So I don't think going with integers will work.
I always thought it was two trucated spheres (of course although the trucations are equal in size, they are on different spots on the sphere) joined at the truncation.

Posted by Gamer
on 20040701 22:59:44 