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Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.

3 votes
0 answers
176 views

What is the expected size of the complement of the union of random cosets of the prime ideal...

For each rational prime $p$ let $\mathbf{X}_p$ denote the random variable uniformly distributed in $\{0, 1, ..., p-1\}$, with all the $\mathbf{X}_p$ independent of each other. Define the coset $\mathb …
4 votes

Google question: In a country in which people only want boys

A colleague, Eugene Salamin, came up with what I would consider the "Book" solution: Phooey, this isn't at all a mathematical puzzle. A social convention cannot override biology, so the proportion …
Daniel Asimov's user avatar
0 votes

Google question: In a country in which people only want boys

The correct answer has nothing to do with the number of families. This is a very tricky problem, and many people fall into the trap of trying to average each possible fraction of girls, weighted only …
Daniel Asimov's user avatar
3 votes

A problem of an infinite number of balls and an urn

The reason this problem has the generally accepted answer of 0 balls in the jug at midnight -- among mathematicians -- is that for any given ball, one may follow its itinerary: at some point it goes i …
Daniel Asimov's user avatar