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# hw1 - Stat 310A/Math 230A Theory of Probability Homework 1...

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Stat 310A/Math 230A Theory of Probability Homework 1 Andrea Montanari Due on September 30, 2010 Solutions should be complete and concisely written. Please, use a separate sheet (or set of sheets) for each problem. Staple sheets referring to the same problem, and write your name on each sheet. You are welcome to discuss problems with your colleagues, but should write and submit your own solution. In some cases, multiple homework options will be proposed (and indicated as ‘Option 1’, ‘Option 2’, etc.). You are welcome to work on all the problems proposed (solutions will be posted), but should submit only those corresponding to one ‘Option’. Option 1: Exercises on measure spaces Solve Exercises [1.1.4], [1.1.13], [1.1.21], [1.1.22] and [1.1.33] in Amir Dembo’s lecture notes. Option 2: The Banach-Tarski paradox in one dimension The objective of this homework is to prove a simplified version of the Banach-Tarski paradox, in the case of the real line. The definition of equidecomposable subsets of R is provided below.

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hw1 - Stat 310A/Math 230A Theory of Probability Homework 1...

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