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Unformatted text preview: C.D. Cutler STAT 333 The Mouse Example Revisited A mouse is in the centre of a maze. Four doors lead out from the centre. Door i , for i = 1 , 2 , 3 opens to a path of length i metres which returns back to the centre of the maze. Door 4 opens to a path of length 4 metres which ends at the only exit from the maze. For some reason the doors are not equally attractive to the mouse (perhaps they are different sizes) and the probability he will choose door i is p i = i/ 10, i = 1 , 2 , 3 , 4. (I just made these probabilities up.) Thus, if he chooses door 4, he scampers 4 metres down the path, exits the maze, and the game is over. If he selects door i , however, for any of i = 1 , 2 , 3, he travels i metres and finds himself back at the centre of the maze. At this point the process undergoes a renewal: that is, the game starts all over again, with the mouse selecting a door again according to the same distribution p i , i = 1 , 2 , 3 , 4 , independent of the past. This is a crucial assumption which may or may not be true in practice. If a person were trappedThis is a crucial assumption which may or may not be true in practice....
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This note was uploaded on 07/12/2010 for the course STAT 333 taught by Professor Chisholm during the Winter '08 term at Waterloo.
- Winter '08