Unit 3

Modeling Random Motion

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Sections:

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 statements: The result of a coin flip is not random, because there are only two possible outcomes. True or False? The result of rolling a 6-sided die is not random, because there are only six possible outcomes. True or False? Whether I win the state Lottery or not is random, because there are so many people playing the Lottery at the same time. True or False? The weather is random, because so many conditions affect the weather that we cannot predict it. True or False?

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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Next: 3.1 - Measuring Randomness