Answered: The Euler totient function : N→ N is… | bartleby

Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 64E

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please put excel screenshot here if you use excel to slove question c

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.,
(1) = 1. Let X be a random number uniformly chosen from {1, 2,..., 20}, and Y =
(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) Ppy (k)
1
2
:
(9) = 6,
(X).
(c) Compute the expected value and variance of Y. (Hint: excel could be helpful.)

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