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Question: Suppose we sample m indices from {1, . . . , n} uniformly at random and with repetition. What is the probability that none of these indices is a correct answer?

Question: Suppose we sample m indices from {1, . . . , n} uniformly at random and with repetition. What is the probability that none of these indices is a correct answer?

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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Question: Suppose we sample m indices from {1, . . . , n} uniformly at random and with repetition. What is the
probability that none of these indices is a correct answer?

Problem 2. Suppose we have an array A[1 : n] which consists of numbers {1,..., n} written in some arbitrary order (this means that A is a permutation of the set {1,...,n}). Our goal in this problem is to design a very fast randomized algorithm that can find an index i in this array such that A[i] mod 8 E {1,2}, i.e., the reminder of dividing A[i] by 8 is either 1 or 2. For simplicity, in the following, we assume that n itself is a multiple of 8 and is at least 8 (so a correct answer always exist). For instance, if n = 8 and the array is A = [8,7, 2, 5, 4, 6, 3, 1], we want to output either of indices 3 or 8.
Transcribed Image Text:Problem 2. Suppose we have an array A[1 : n] which consists of numbers {1,..., n} written in some arbitrary order (this means that A is a permutation of the set {1,...,n}). Our goal in this problem is to design a very fast randomized algorithm that can find an index i in this array such that A[i] mod 8 E {1,2}, i.e., the reminder of dividing A[i] by 8 is either 1 or 2. For simplicity, in the following, we assume that n itself is a multiple of 8 and is at least 8 (so a correct answer always exist). For instance, if n = 8 and the array is A = [8,7, 2, 5, 4, 6, 3, 1], we want to output either of indices 3 or 8.
Expert Solution
Introduction :

Given :

  • Number of samples = n
  • Number of values sampled = m
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