There is an east-west 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?

My formula for 2 It should be (3L-5)/(L-1)
This is in agreement with Charlie's simulation.

I'm having problems with my general formula for 3
I did L = 3.25 though and got the exact solution (5.75-4ln(1.25))/2.25 which agrees with Charlies simulation to 2 decimal places.

I can usually go through my steps from a single case to a general formula but this time something is going wrong. I plan to keep at it. The natural log arises from integrating a function derived from the 2
-Jer

Posted by Jer on 2004-07-02 15:15:23