An unfair coin has probability of landing heads. As an experiment, the coin is thrown repeatedly,...
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An unfair coin has probability of landing heads. As an experiment, the coin is thrown repeatedly, until the first time it lands tails, after which the experiment ends. Suppose that this full experiment is conducted n times in total, dur- ing which the total number of coin throws is N (this includes all n experiments). (a) Name a probability distribution that is related to the number of throws in a single experiment. (2 marks) (b) Explain in words why we can expect that, on average, 3N/5 = n. (8 marks) (c) Use part (b) to explain why the expected number of throws in a single experiment is 5/3. (5 marks) (d) Now suppose that the experiment is modified so that it stops only after 500 coins have landed tails, and before each throw, the thrown coin is selected randomly between two coins (each with probability 0.5) : one coin has probability of landing heads and the other coin has probability of landing heads. By modifying the arguments you used in (b) and (c), or other- wise, find the expected total number of throws for the full modi- fied experiment to be performed 6 times in a row. (10 marks) An unfair coin has probability of landing heads. As an experiment, the coin is thrown repeatedly, until the first time it lands tails, after which the experiment ends. Suppose that this full experiment is conducted n times in total, dur- ing which the total number of coin throws is N (this includes all n experiments). (a) Name a probability distribution that is related to the number of throws in a single experiment. (2 marks) (b) Explain in words why we can expect that, on average, 3N/5 = n. (8 marks) (c) Use part (b) to explain why the expected number of throws in a single experiment is 5/3. (5 marks) (d) Now suppose that the experiment is modified so that it stops only after 500 coins have landed tails, and before each throw, the thrown coin is selected randomly between two coins (each with probability 0.5) : one coin has probability of landing heads and the other coin has probability of landing heads. By modifying the arguments you used in (b) and (c), or other- wise, find the expected total number of throws for the full modi- fied experiment to be performed 6 times in a row. (10 marks)
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Related Book For
Discovering Advanced Algebra An Investigative Approach
ISBN: 978-1559539845
1st edition
Authors: Jerald Murdock, Ellen Kamischke, Eric Kamischke
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