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IE143-LQ2reviewprobs

# IE143-LQ2reviewprobs - University of the Philippines...

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University of the Philippines – Diliman Department of Industrial Engineering and Operations Research IE 143 Long Quiz 2 Long Quiz 2 Review Problems 1. Three white and three black balls are distributed in two urns in such a way that each contains three balls. At each step, we draw one ball from each urn and place the ball drawn from the first urn into the second, and conversely with the ball from the second urn. Construct the transition probability matrix if we say that the system is in state i, i = 0, 1, 2, 3 if the first urn contains i white balls. (++) 2. Suppose that if it has rained for all of the past three days, then it will rain today with probability 0.8; if it did not rain for any of the past three days, then it will rain today with probability 0.2; and in any other case the weather today will, with probability 0.6, be the same as the weather yesterday. Construct the transition probability matrix for this Markov chain. (++) 3. 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 or coin 2, then what is the probability that the coin flipped on the third day after the initial flip is coin 1? (+) 4. Suppose in problem 3 that the coin flipped on Monday comes up heads. What is the probability that the coin flipped on Friday of the same week also comes up heads? (+) 5. On any given day Gary is cheerful ( C ), so-so ( S ), or glum ( G ). If he is cheerful today, then he will be C , S , or G tomorrow with respective probabilities 0.5, 0.4, 0.1. If he is feeling so-so today, then he will be

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