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Assignment 6 - CE93-Engineering Data Analysis Joan Walker...

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CE93-Engineering Data Analysis Joan Walker, Spring 2011 Assignment 6 Due Wednesday, March 9 th , 2011, 11:10 AM 1. Consider the following game: A fair coin is flipped until the first tail appears; we win $2 if it appears on the first toss, $4 if it appears on the second toss, and, in general, $2 k if it first occurs on the k th toss. Let the random variable X denote our winnings. If a fair game is one where the expected earnings, winnings minus payment to play, equals 0, how much should we have to pay up front in order for this to be a fair game? Would you play this game for this price? Realistically, would you play this game for even a small fraction of this price? [Hint: The answer to the last question may not be as it seems] 2. A wastewater treatment plant (WWTP) treats water from primarily two distinct sources, one from stormwater, and two from human sources (including residential, commercial, and industrial wastewater). Let X be the amount of flow of wastewater from stormwater, and let Y be the amount of flow of wastewater from human sources. Given the following information:
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