Hw3_ORIE361_2008

Hw3_ORIE361_2008 - ORIE 361/523 Homework 3 Instructor: Mark...

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ORIE 361/523 – Homework 3 Instructor: Mark E. Lewis due February 13, 2008 (drop box) 1. A fair coin is tossed repeatedly with results Y 0 ,Y 1 ,Y 2 ,... that are 0 and 1 with probability 1 / 2 each. For n 1, let X n = Y n + Y n - 1 be the number of 1 0 s in the ( n - 1) st toss and n th toss. Is X n a Markov Chain ? Prove or disprove. 2. Suppose that coin 1 has probability 0.7 of coming up heads, and coin 2 has probability 0.6 of coming up heads. If the coin flipped today comes up heads, then we select coin 1 to flip tomorrow, and if it comes up tails, then we select coin 2 to flip tomorrow. If the coin initially flipped is equally likely to be coin 1 and coin 2, then what is the probability that the coin flipped on the third day (day 3) after the initial flip (initial flip occurs on day 0), is coin 1? 3. The Media Police have identified 6 states associated with television watching: 0 (never watch tv), 1 (watch only PBS), 2 (watch tv fairly frequently), 3 (addict), 4 (undergoing behavior modification), 5 (brain dead). Transitions from state to state can be modelled as a
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This note was uploaded on 03/01/2010 for the course ORIE 361 taught by Professor Lewis,m. during the Spring '07 term at Cornell.

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Hw3_ORIE361_2008 - ORIE 361/523 Homework 3 Instructor: Mark...

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