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316_F07_HW2

# 316_F07_HW2 - IOE 316 Fall 2007 Homework 2 Due November 6...

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IOE 316 Fall 2007 – Homework 2 Due November 6, 2007 1. (15 points) Consider the following Markov chain: (a) (5 points) Find the values of x and y . (b) (10 points) Find 2-step transition probability matrix P 2 2. (25 points) A Markov chain { X n , n 0 } with states 0 , 1 , 2, has the transition probability matrix P = 1 2 1 6 1 3 0 2 3 1 3 1 2 0 1 2 If P { X 0 = 0 } = P { X 0 = 1 } = 1 4 , find E [ X 3 ]. 3. (20 points) On any given day IOE student is either cheerful (C), so-so (S), or glum (G). If she is cheerful today, then she will be C, S, or G tomorrow with respective probabilities 0.5, 0.4, 0.1. If she is feeling so-so today, then she will be C, S, or G tomorrow with probabilities 0.3, 0.4, 0.3. If the student is glum today, then she will be C, S, or G tomorrow with probabilities 0.2, 0.3, 0.5. The IOE student is currently in a cheerful mood. What is the probability that she is not in a glum mood on any of the following three days? 1

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4. (30 points) Suppose that coin 1 has probability 0.6 of coming up heads, and coin 2 has probability 0.7 of coming up heads. If the coin flipped today comes up heads, then we select
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