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
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Transcribed Image Text:Exercise 6.
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
questions, i.e., do not mix up 6.1 and 6.2. Moreover, do not confuse the
number of coin flips with the number of coins.
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