A random bit is a probability space with 2 elementary events, each appearing with probability 1/2. More informally, think of flipping an unbiased coin. Suppose that random bits are available, but we want to simulate an event. with probability 1/3. 6.1. Can you simulate an event with probability 1/3, by using some fired finite number of random bits? 6.2. Give a randomized algorithm that simulates an event with probability 1/3 by using some expected finite number of random bits. Try to make this expected number as small as you can. In both 6.1 and 6.2: Do not only give the answers but explain them, e.g., say why you think that the task in 6.1 is possible or impossible, and prove that your algorithm in 6.2 has the claimed properties. Stick exactly to the

A random bit is a probability space with 2 elementary events, each appearing with probability 1/2. More informally, think of flipping an unbiased coin. Suppose that random bits are available, but we want to simulate an event. with probability 1/3. 6.1. Can you simulate an event with probability 1/3, by using some fired finite number of random bits? 6.2. Give a randomized algorithm that simulates an event with probability 1/3 by using some expected finite number of random bits. Try to make this expected number as small as you can. In both 6.1 and 6.2: Do not only give the answers but explain them, e.g., say why you think that the task in 6.1 is possible or impossible, and prove that your algorithm in 6.2 has the claimed properties. Stick exactly to the

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter9: Counting And Probability

Section9.3: Binomial Probability

Problem 2E: If a binomial experiment has probability p success, then the probability of failure is...

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