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Extend Example 1.4-6 to an n-sided die. That is, suppose

Probability and Statistical Inference | 9th Edition | ISBN: 9780321923271 | Authors: Robert V. Hogg, Elliot Tanis, Dale Zimmerman ISBN: 9780321923271 41

Solution for problem 19E Chapter 1.4

Probability and Statistical Inference | 9th Edition

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Probability and Statistical Inference | 9th Edition | ISBN: 9780321923271 | Authors: Robert V. Hogg, Elliot Tanis, Dale Zimmerman

Probability and Statistical Inference | 9th Edition

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Problem 19E

Extend Example 1.4-6 to an \(n\)-sided die. That is, suppose that a fair \(n\)-sided die is rolled \(n\) independent times. A match occurs if side \(i\) is observed on the \(i\) th trial, \(i=1,2, \ldots, n\).

(a) Show that the probability of at least one match is

       \(1-\left(\frac{n-1}{n}\right)^{n}=1-\left(1-\frac{1}{n}\right)^{n}\).

(b) Find the limit of this probability as n increases without bound.

Equation Transcription:

.

Text Transcription:

n  

i  

i=1,2,,n  

1-(n-1/n)^n=1-(1-1/n)^n

Step-by-Step Solution:

Answer

Step 1 of 3

For a normal die probability that there are no matches is ⅚

If it is rolled 6 times the probability that there are no matches is 6


Step 2 of 3

Chapter 1.4, Problem 19E is Solved
Step 3 of 3

Textbook: Probability and Statistical Inference
Edition: 9
Author: Robert V. Hogg, Elliot Tanis, Dale Zimmerman
ISBN: 9780321923271

This full solution covers the following key subjects: match, die, sided, Probability, Bound. This expansive textbook survival guide covers 59 chapters, and 1476 solutions. Since the solution to 19E from 1.4 chapter was answered, more than 746 students have viewed the full step-by-step answer. Probability and Statistical Inference was written by and is associated to the ISBN: 9780321923271. This textbook survival guide was created for the textbook: Probability and Statistical Inference , edition: 9. The answer to “?Extend Example 1.4-6 to an \(n\)-sided die. That is, suppose that a fair \(n\)-sided die is rolled \(n\) independent times. A match occurs if side \(i\) is observed on the \(i\) th trial, \(i=1,2, \ldots, n\).(a) Show that the probability of at least one match is \(1-\left(\frac{n-1}{n}\right)^{n}=1-\left(1-\frac{1}{n}\right)^{n}\).(b) Find the limit of this probability as n increases without bound.Equation Transcription:.Text Transcription:n i i=1,2,,n 1-(n-1/n)^n=1-(1-1/n)^n” is broken down into a number of easy to follow steps, and 63 words. The full step-by-step solution to problem: 19E from chapter: 1.4 was answered by , our top Statistics solution expert on 07/05/17, 04:50AM.

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Extend Example 1.4-6 to an n-sided die. That is, suppose