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This discussion relates to Exercise 24 in Chapter 11 concerning "Kemeny's Constant" and the question: Should Peter have been given the prize?
In the historical remarks for section 6.1, Grinstead and Snell describe Huygen's approach to expected value. The were based on Huygen's book The Value of all Chances in Games of Fortune which can also be found here. Peter reworks Hygen's discussion to show connections with modern ideas such fair markets and hedging. He illustrate the limitation of hedging using a variant of the St. Petersburg Paradox.
In Feller's Introduction to Probability theory and Its Applications, volume 1, 3d ed, p. 194, exercise 10, there is formulated a version of the local limit theorem which is applicable to the hypergeometric distribution, which governs sampling without replacement. In the simpler case of sampling with replacement, the classical DeMoivre-Laplace theorem is applicable. Feller's conditions seem too stringent for applications and are difficult t to prove. It is the purpose of this note to re-formulate and prove a suitable limit theorem with broad applicability to sampling from a finite population which is suitably large in comparison to the sample size.
These are programs to demonstrate basic ideas of probability and statistics that can be run from the Web using one of the standard browsers. We will try to keep here only programs that work and do not crash your computer too often.
This is the homepage for Chance Magazine. This is a magazine of the American Statistical Association published by Springer-Verlag. Chance Magazine may be considered the "Scientific American" of probability and statistics.
A source for all that's new in Interacting Particle Systems. Each week you find a new and beautiful graphical picture and the recipe that produced it. Show your students what fun they can have if they continue their study of probability.