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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