The Euler totient function : N→ N is defined by o(n) = #{k≤n: gdc(n, k) = 1}. That is, (n) is the count of all positive integer k that is relatively prime to n. E.g., (9) = 6, (1) = 1. Let X be a random number uniformly chosen from {1,2,..., 20}, and Y = o(X). (a) Find the range of Y. (b) Find the probability mass function of Y. Present your answer in a table, e.g., ke range(Y) Py (k) 1 2 ⠀ (c) Compute the expected value and variance of Y. (Hint: excel could be helpful.)
The Euler totient function : N→ N is defined by o(n) = #{k≤n: gdc(n, k) = 1}. That is, (n) is the count of all positive integer k that is relatively prime to n. E.g., (9) = 6, (1) = 1. Let X be a random number uniformly chosen from {1,2,..., 20}, and Y = o(X). (a) Find the range of Y. (b) Find the probability mass function of Y. Present your answer in a table, e.g., ke range(Y) Py (k) 1 2 ⠀ (c) Compute the expected value and variance of Y. (Hint: excel could be helpful.)
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 32E
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