# rec03 - Massachusetts Institute of Technology Department of...

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Massachusetts Institute of Technology 6.041/6.431: Probabilistic Systems Analysis (Fall 2010) Recitation 3: September 16, 2010 1. Example 1.20, page 37 in the text. Consider two independent fair coin tosses, in which all four possible outcomes are equally likely. Let H 1 = { 1st toss is a head } , H 2 = { 2nd toss is a head } , D = { the two tosses produced diFerent results } . (a) Are the events H 1 and H 2 (unconditionally) independent? (b) Given event D has occurred, are the events H 1 and H 2 (conditionally) independent? 2. Imagine a drunk tightrope walker, in the middle of a really long tightrope, who manages to keep his balance, but takes a step forward with probability p and takes a step back with probability (1 - p ). (a) What is the probability that after two steps the tightrope walker will be at the same place on the rope? (b) What is the probability that after three steps, the tightrope walker will be one step forward

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rec03 - Massachusetts Institute of Technology Department of...

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