Modeling Random Motion
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3.1 - Measuring Randomness
3.2 - Observed Distributions
3.3 - Random Walks
3.4 - Pascal's Triangle
3.5 - Measuring Average Distances
3.6 - Proving Average Squared Difference (Optional)
3.7 - The Wandering Ant on a Square Grid
3.8 - Models in Science
3.9 - What Do You Think?
3.10 - Research Projects
What does "random'' mean? Think carefully before you answer! The definition may not be as obvious as you think.
Q3.1: After checking the dictionary definition, consider the following four
The main theme of this site is the study of how order grows out of randomness. Every structure in your body grows and every process in your body takes place in the presence of randomly-agitated molecules. Yet instead of being torn apart by this randomness, we survive. We even thrive on the randomness of nature. How can this be? Before we can begin to answer this question, we must study randomness itself, and details of the staggering, zigzag paths that atoms and molecules execute all around us.
Can order grow out of randomness? Think about the following question:
Q3.2: Consider a group of 20 people. We want to divide
the group into two groups, group A and group B. Each group
should have 10 members. Now flip a coin for each person:
heads, the person goes to group A; tails, the person goes
to group B. Will the people end up evenly divided, ten
in each group? Could they all end up in one group? Which
of these results is more likely?
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