Binomial Distribution, Diffusion, Central Limit Theorem
The object of this problem is to see the relationship between random walks, the binomial distribution, and the normal (Gaussian) distribution.
- 1. Create NumAve random walks and record their final endpoint.
- 2. Make a histogram of the endpoints.
- 3. Compare the result with the exact result obtained by applying the binomial distribution. Nelson's book has a discussion of this as do a large number of books on introductory statistical physics, Berg Links to an external site. and, of course, the web.
- 4. Plot the results.
- 5. Compare the exact result to that obtained for a Gaussian with the correct variance. The fact that this approaches a Gaussian is an example of the "Centeral Limit Theorem".
- 6. Give an example of a biological experiment where it is reasonable to assume that a measurement is distributed as a Gaussian, and an example where you would not expect a Gaussian distribution.
Look at this hints file Download hints file. Much of the code is already written and you need to fill it in by calculating the appropriate formulas. Plot the results and upload them.