All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars
 perplexus dot info

 Seeing red (Posted on 2008-06-07)

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 Rating: 5.0000 (1 votes)

 Subject Author Date re: error in solution Harry 2009-03-19 20:00:02 re(2): error in solution Eigenray 2008-06-10 19:53:05 re: error in solution FrankM 2008-06-10 12:28:17 error in solution Eigenray 2008-06-09 16:26:14 Power in independence Gamer 2008-06-08 21:43:26

 Search: Search body:
Forums (0)
Random Problem
Site Statistics
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox: