Author: Dan Homan
Date: 07:17:11 08/17/98
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It seemed clear to me that you defined the trials as separate units, on re-reading I see that "20 in a row" could stretch across trials. If you would like to work out this case, let me know the answer. You asked me to reconsider my answer for (c), but I didn't answer (c). In c) it is quite ambiguous what you meant by "the chance this result does not contradict the fair coin hypothesis", so I simply gave you the probability of getting 4 trials of "20 in a row" in an N-trial experiment. My "off-my-head" statistics knowledge is not good enough to answer such an ill-posed question - so I gave you the best information that I could... please let me know the final result. In (d) I simply set the dispersion of a N-trial result equal to 1 and solved for N. This is a ball-park figure, I know, but it was the best I could do sitting at the computer screen. If you have a better result, please let me know. This was obviously more of an exercise in word games than statistics. I'm not sure what point you are making, except the obvious one that these questions need to be well defined or we will all talk right past one another. - Dan P.S. Here is an interesting story about physists and mathematicians.... There was a famous physist (I can't remember his name) who claimed to be able to tell a physist from a mathematician by how they answered the following question: Two brothers live 10 miles apart. They both leave their houses one day, at the same time, and walk on a straight line towards one another. Each brother is walking at 4 miles an hour. One brother has a dog who leaves his house with him. The dog is running at 8 miles an hour. When the dog reaches the other brother, he turns around and goes back to his owner. When he reaches his owner, he turns around again towards the other brother. The dog keeps up this back and forth travel between the brothers until they meet. How far has the dog traveled? The fellow found that physists will reply with the correct answer instantly, while mathematicians will take several minutes to sum the series before giving the correct answer. He found this to be an excellent descriminator between physists and mathematicians. One day, this famous physist met the reknown mathematician, Jon Von Neumann, to whom he posed this question. Von Neuman replied instantly, which surprised the physist. He asked Von Neumann, "But you are a mathematician, I was sure you would sum the series." To which, Von Neumann replied, "I did." Here is another one: A physist, mathematician, and engineer are given the challenge of enclosing the most area with the shortest length of fence. The engineer promptly forms a circle, stating that it is the most efficient solution. The physist takes the fence and starts making a straight line toward the horizion while mumbling something about one infinity being larger than another. The mathematician thinks for a moment and then makes a very tight circle of fence around himself and states, "I define myself to be in the outside!".
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