practice_mid

practice_mid - Stat 310A/Math 230A Theory of Probability...

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Unformatted text preview: Stat 310A/Math 230A Theory of Probability Practice Midterm Andrea Montanari October 23, 2010 This is a practice midtetm: rules described beow will be the same as for the real Midterm. Solutions wil be posted. Solutions should be complete and concisely written. Please, use a separate booklet for each problem. You have 2 hours but you are not required to solve all the problems!!! Just solve those that you can solve within the time limit. For any clarification on the text, one of the TA’s will be within short distance from the room, and Andrea in Packard 272. You can consult textbooks and your notes. You cannot use computers, and in particular you can not use the web. You can cite theorems from Amir Dembo’s lecture notes by number, and exercises you have done as homework by number as well. Any other non-elementary statement must be proved! Problem 1 Consider the measurable space (Ω , F ), with: Ω = { , 1 } N the set of (infinite) binary sequences ω = ( ω 1 , ω 2 , ω 3 , . . . ); F the σ-algebra generated by cylindrical sets (equivalently the σ-algebra generated by sets of the type A i,x = { ω : ω i = x } for i ∈ N and x ∈ {...
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This note was uploaded on 08/20/2011 for the course STATS 310A at Stanford.

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practice_mid - Stat 310A/Math 230A Theory of Probability...

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