5. An art starts walking from the origin. During each second, it has an equal chance of moving 1 inch right, 2 inches up, 3 inches left, or 4 inches down. What is the ant's expected location after 5 seconds if it starts at the origin?
Not totally sure about this.....but....after one second.....the expected position of the ant can be found as
[ 1(.25) - 3(.25) , 2(.25) - 4(.25) ] = [ -.5, -.5 ]
So....each second, the ant is expected to move 1/2 unit to the left and 1/2 unit down
So....after 5 seconds the expected location is 5 [ -.5, -.5 ] = (-2.5, -2.5)
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Copied from CPHILL from : http://188.8.131.52/questions/super-hard-expected-value-questions