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An ant 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?

 Jun 16, 2019
edited by Oofrence  Jun 16, 2019
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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)

 

 

Do Not give me Credit. Go to the other link and give CPHILL credit cuz he wrote this and im not taking anything for not my work.

 

Copied from CPHILL from : http://209.126.117.101/questions/super-hard-expected-value-questions 

http://209.126.117.101/questions/super-hard-expected-value-questions

 Jun 16, 2019
edited by Melody  Jun 16, 2019

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