Yes, I love Feller's book: < http://www.amazon.com/Introduction-Probability-Theory-Applications-Edition/d... >. It contains many fascinating facts in addition to the arcsine law Thane alludes to in his essay. For example, in the symmetric random walk on Z^n starting from the origin (2n equally likely ways to step), the probability of returning to the origin is 1. If n = 1 or 2, that is. For n >= 3 that probability is < 1. Another one I liked regards the probability that n people's birthdays will cluster within some time interval of a given size (that may run from one year to the next): Take this to be the probability P(n, theta) that n points independently uniformly distributed on the circle will all lie within some arc of angle theta. What I found amazing is that for fixed n, P(n, theta) is a continuous but not everywhere differentiable function of theta. --Dan Thane wrote: << Here's a little meditation on Feller (and his being dead) that I wrote in 1999 < http://www.kothreat.com/1999.06.26.htm >

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