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April 10th, 2009, 07:04 AM   #1
Joined: Apr 2009

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Help me to solve this problem!!!???

*Given a RoboCup field of size 12x20 meters, two robots are placed at random positions. We
would like to know the expected distance between both of them. The position of robot1 can be
expressed by two random variables X1 and Y1; the position of robot2 by X2 and Y2.
X1, X2 are uniformly distributed over [0, 12]
Y1, Y2 are uniformly distributed over [0, 20]
We can define a new random variable D expressing the distance between both robots by D = sqrt(
(X2 - X1)2 + (Y2 - Y1)2 ).
What is the expected value of X1, i.e. E(X1)? How can the expected value of D be determined, either by an
equation or approximated on a computer perhaps?
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