rec10 - Massachusetts Institute of Technology Department of...

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Massachusetts Institute of Technology 6.041/6.431: Probabilistic Systems Analysis (Fall 2010) Recitation 10 October 12, 2010 Question 1. The two parts of this question are about identities for a probabilistic model with sample space Ω, events A and B , and discrete random variable X . Any time conditioning on an event is indicated, the event has positive probability. An identity is true when it holds without any additional restrictions; it is false when there is any counterexample. 1.1. Which one of the following statements is true ? (a) P ( A B ) may be larger than P ( A ). (b) The variance of X may be larger than the variance of 2 X . (c) If A c B c = , then P ( A B ) = 1. (d) If A c B c = , then P ( A B ) = P ( A ) P ( B ). (e) If P ( A ) > 1 / 2 and P ( B ) > 1 / 2, then P ( A B ) = 1. 1.2. Which one of the following statements is true ? (a) If
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This note was uploaded on 12/02/2011 for the course ENGINEERIN EE302 taught by Professor Proasin during the Spring '11 term at South Carolina.

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rec10 - Massachusetts Institute of Technology Department of...

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