Function Analysis: Example 2
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Description How it works Examples: Reaction Kinetics 1-D Random Walk Analysis of Noisy Data |
1- Dimensional Random WalkA random walk or "drunkard's walk" is a movement where successive steps are taken at random. Random walk is used to model many phenomena, not only in physics but also in economics, biology and gambling. This wiki page gives a good introduction to random walk and its applications. Here we consider a 1-dimensional random walk. Imagine a drunkard moving along a straight line, perhaps a railway track. He takes a sequence of steps, each step is of equal length but could be in the forward or backward directions. After a long time, where would he be? The answer of course, is that we don't know, since the direction is random. But on the average, where can we expect him to be ? Lets use the Function Analysis tool to find out. To model the random walk, we use the function: =IF(RAND()>0.5,1,-1) and enter the range as 0 to 1000. The initial value of the integral is 0. The plot of the integral gives the location of the person at the end of 1000 steps. It looks like this:  To generate another set of random steps, simple press F9, the spreadsheet recalculates and another graph is obtained. We note that most of the time, the distance covered at the end of 1000 steps ranges from 25 to 35. |