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Seeing red (Posted on 2008-06-07) Difficulty: 2 of 5

The interior of the square [0,1] x [0,1] is initially coloured white.

Four random numbers: u,v,x,y in the range [0,1] are selected and the points inside the rectangle formed by the corners (u,v), (x,y), (u,y), (x,v) are recoloured: areas painted white are repainted red, and areas painted red are repainted white.

This recolouring procedure is repeated N times. Show that the expectation value of the red area is given by the formula:

1/2 - 1/2 ∫ dA ∫ dB {1 - 2 A (1-A) B (1-B)}N

where both integrals go from 0 to 1.

See The Solution Submitted by FrankM    
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Comments: ( You must be logged in to post comments.)
  Subject Author Date
re: error in solutionHarry2009-03-19 20:00:02
re(2): error in solutionEigenray2008-06-10 19:53:05
Questionre: error in solutionFrankM2008-06-10 12:28:17
error in solutionEigenray2008-06-09 16:26:14
Some ThoughtsPower in independenceGamer2008-06-08 21:43:26
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