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4. For this problem, consider the following process. Suppose we have n many unique integer numbers in an array. Suppose we pick a number at random. Let S be the set of numbers that are smaller than the chosen number. (a) What is the expected size of S? (b) Suppose we apply the same process again on the set S. We repeat the process k times. What is the expected size of S after applying the process k times in terms of k ?

4. For this problem, consider the following process. Suppose we have n many unique integer numbers in an array. Suppose we pick a number at random. Let S be the set of numbers that are smaller than the chosen number. (a) What is the expected size of S? (b) Suppose we apply the same process again on the set S. We repeat the process k times. What is the expected size of S after applying the process k times in terms of k ?

A First Course in Probability (10th Edition)
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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Please do not rely too much on chatgpt, because its answer may be wrong. Please consider it carefully and give your own answer. You can borrow ideas from gpt, but please do not believe its answer.Very very grateful!Please do not rely too much on chatgpt, because its answer may be wrong. Please consider it carefully and give your own answer. You can borrow ideas from gpt, but please do not believe its answer.Very very grateful!

4. For this problem, consider the following process. Suppose we have n many unique integer numbers in an array. Suppose we pick a number at random. Let S be the set of numbers that are smaller than the chosen number. (a) What is the expected size of S? (b) Suppose we apply the same process again on the set S. We repeat the process k times. What is the expected size of S after applying the process k times in terms of k ?
Transcribed Image Text:4. For this problem, consider the following process. Suppose we have n many unique integer numbers in an array. Suppose we pick a number at random. Let S be the set of numbers that are smaller than the chosen number. (a) What is the expected size of S? (b) Suppose we apply the same process again on the set S. We repeat the process k times. What is the expected size of S after applying the process k times in terms of k ?
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