Homework Help is Here – Start Your Trial Now!
Math
Probability
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.)

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...
See similar textbooks
icon
Related questions
Question
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.)
Transcribed Image Text: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.)
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer