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Unformatted text preview: Statistical Physics I (8.044) Spring 2009 Assignment 3 February 18, 2009 Due February 25, 2009 Please remember to put your name and section number at the top of what you turn in. Readings By now you should be completing your reading of the Notes on Probability by Prof. Greytak. You will need to have read the first three sections of these notes for this problem set. Problem Set 3 1. Rolling Dice (6 points) You roll two dice. Each individual die can come up 1, 2, 3, 4, 5 or 6. Assume that each of these six outcomes is equally probable. Call the sum of the two dice S . S is a discrete random variable that can take on values 2, 3, 4, . . . 12. Find the mean, variance, and standard deviation of S . 2. The Original Poisson Distribution (6 points) According to Blundell and Blundell the data that motivated Poisson 1 to discover what we now call the Poisson distribution was connected with the probability of a soldier in the Prussian army being kicked to death by a horse. The number of horse-kick deaths of Prussian military personnel was recorded for each of 10 corps in each of 20 years. The number of deaths per year per corps was zero in 109 cases, one in 65 cases, two in 22 cases, three in 3 cases and four in 1 case. Calculate the mean number of deaths per year per corps. Assume the number of deaths per year per corps is Poisson distributed with this mean, and compute how many instances (out of 200) of zero, one, two, three and four deaths per year per corps you would expect. Compare your Poissonian prediction to the actual data. 3. Bose-Einstein Statistics (10 points) You learned in 8.03 that the electromagnetic field in a cavity can be decomposed (as a three-dimensional Fourier series) into a countably infinite number of modes, each 1 I did not check the original literature to confirm this, and in fact I am skeptical as to whether Blundell and Blundell are correct that this is what motivated Poisson. The first reference to horse-kick deaths in the Prussian army as an application of the Poisson distribution that I found, after a very quick Google search, is an 1898 analysis by Bortkiewicz from which the numbers in this problem originate. Poisson himself diedis an 1898 analysis by Bortkiewicz from which the numbers in this problem originate....
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This note was uploaded on 09/17/2009 for the course PHYSICS 8.044 taught by Professor Krishnarajagopal during the Spring '09 term at MIT.
- Spring '09