RandomWalk - Version Fall 2008, Not Complete yet The Random...

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The Random Walk and Diffusion One-Dimensional Random Walk Imagine a path of equally-spaced stepping stones: …… ……. . You start a random walk by standing on one stepping stone and tossing a fair coin. If it comes up heads, you take a step to the right, if it comes up tails, you take a step to the left. You repeat tossing the coin and let probability determine where you will end up. H = Step Right T = Step Left ± +1 -1 Here is the result of 16 coin tosses: Toss # 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Result H T H T H T T H T H T T T H T T Location 1 0 1 0 1 0 -1 0 -1 0 -1 -2 -3 -2 -3 -4 In this example, you start at position 0 and after the sequence of 16 random steps end up at position –4. If you repeated this experiment, you would probably end up with a different sequence of heads and tails, and end up at a different location. There is a small probability that you will toss all heads, and end up at a location +16 from the starting point. There is an equally small probability that you will toss all tails and end up at a location –16 from the starting point. The highest probability is that you end up back at the starting point. This is very similar to a demonstration that you might have seen at a science museum where a ball is dropped straight down onto a horizontal peg, and then falls either to the right or to the left. It then hits a second peg and again falls to the right or left, and so on. 0
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This note was uploaded on 11/28/2010 for the course MTE 209 taught by Professor Tanyafalten during the Fall '09 term at Cal Poly Pomona.

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RandomWalk - Version Fall 2008, Not Complete yet The Random...

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