3.4 - Pascal's Triangle

SimuLabs:

5. Random Walk and Pascal's Triangle

7.
Average Position after *N* steps

In
the preceding section we found that some predictability grows out
of random coin flipping, leading to a "bell-shaped'' bar graph
of the results. Such a distribution is also called the *normal
* or * Gaussian * distribution (you will encounter this
distribution at many places in this site). This section carries
the idea further, relating random coin flipping to random motion.
Random movement is important for understanding the microscopic world
in nature, because atoms and molecules move randomly. How can we
describe the random motion of molecules in, say, a gas? Molecules
are too small to see, so to help us think concretely we replace
a molecule with something we can see: a wandering ant. If a wandering
ant starts at a lamp post and takes steps of equal length along
the street, how far will it be from the lamp post after a certain
number, say N, steps? Though this question is seemingly trivial,
it poses one of the most basic problems in statistical science.