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316_F07_HW3 - IOE 316 Fall 2007 Homework 3 Due 1(25 points...

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IOE 316 Fall 2007 – Homework 3 Due November 13, 2007 1. (25 points) Coin 1 comes up heads with probability 0.7 and coin 2 with probability 0.5. A coin is continually flipped until it comes up tails, at which time that coin is put aside and we start flipping the other one. (a) (10 points) What portion of flips use coin 1? (b) (5 points) If we start the process with coin 2, what is the expected number of flips until we go back to flipping coin 2? (c) (10 points) If we start the process with coin 1, what is the probability that coin 2 is used on the sixth flip? 2. (15 points) Suppose that whether or not it rains today depends on previous weather conditions through the last two days. Specifically, suppose that if it rained for the past two days, then it will rain tomorrow with probability 0.8; it it rained today but not yesterday, then it will rain tomorrow with probability 0.6; if it rained yesterday but not today, then it will rain tomorrow with probability 0.3; if it has not rained in the past two days, then it will rain tomorrow with probability 0.2. Calculate the proportion of days that it rains.
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