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Initially, the integer 80 is written on a blackboard. At each step, the integer x on the blackboard is replaced with an integer chosen uniformly at random among [0, x - 1], unless x = 0, in which case it is replaced by an integer chosen uniformly at random among [0, 2024]. Let P(a, b) be the probability that after a steps, the integer on the board is b. Determine lim P(a, 80) a+ P(a, 2024) ( P(a,80) (that is, the value that the function (a.2024) approaches as a goes to infinity). Your solution: dba (c) to our you 10] (*=

Initially, the integer 80 is written on a blackboard. At each step, the integer x on the blackboard is replaced with an integer chosen uniformly at random among [0, x - 1], unless x = 0, in which case it is replaced by an integer chosen uniformly at random among [0, 2024]. Let P(a, b) be the probability that after a steps, the integer on the board is b. Determine lim P(a, 80) a+ P(a, 2024) ( P(a,80) (that is, the value that the function (a.2024) approaches as a goes to infinity). Your solution: dba (c) to our you 10] (*=

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.7: Introduction To Coding Theory (optional)
Problem 7E
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Initially, the integer 80 is written on a blackboard. At each step, the integer x on the blackboard is replaced with an integer chosen uniformly at random among [0, x - 1], unless x = 0, in which case it is replaced by an integer chosen uniformly at random among [0, 2024]. Let P(a, b) be the probability that after a steps, the integer on the board is b. Determine lim P(a, 80) a+ P(a, 2024) ( P(a,80) (that is, the value that the function (a.2024) approaches as a goes to infinity). Your solution: dba (c) to our you 10] (*=
Transcribed Image Text:Initially, the integer 80 is written on a blackboard. At each step, the integer x on the blackboard is replaced with an integer chosen uniformly at random among [0, x - 1], unless x = 0, in which case it is replaced by an integer chosen uniformly at random among [0, 2024]. Let P(a, b) be the probability that after a steps, the integer on the board is b. Determine lim P(a, 80) a+ P(a, 2024) ( P(a,80) (that is, the value that the function (a.2024) approaches as a goes to infinity). Your solution: dba (c) to our you 10] (*=
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