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An ecologist wishes to mark off a circular sampling region

Probability and Statistics for Engineers and the Scientists | 9th Edition | ISBN: 9780321629111 | Authors: Ronald E. Walpole; Raymond H. Myers; Sharon L. Myers; Keying E. Ye ISBN: 9780321629111 32

Solution for problem 21E Chapter 4

Probability and Statistics for Engineers and the Scientists | 9th Edition

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Probability and Statistics for Engineers and the Scientists | 9th Edition | ISBN: 9780321629111 | Authors: Ronald E. Walpole; Raymond H. Myers; Sharon L. Myers; Keying E. Ye

Probability and Statistics for Engineers and the Scientists | 9th Edition

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Problem 21E

An ecologist wishes to mark off a circular sampling region having radius 10 m. However, the radius of the resulting region is actually a random variable ?R ?with pdf What is the expected area of the resulting circular region?

Step-by-Step Solution:

Answer Step 1 of 2 11 11 3 2 E(r)= rf(r) dr = 4(1 (10 r )) dr 9 9 11 3r 2 = 4 (r 9) dr 9 4 2 11 = 3 r 9r 4 [ 43 2 ]9 3 114 9(11 ) 94 9(9 ) = 4( 4 2 ) (4 2 )} 3 7361 = 4 4 )=1380.18

Step 2 of 2

Chapter 4, Problem 21E is Solved
Textbook: Probability and Statistics for Engineers and the Scientists
Edition: 9
Author: Ronald E. Walpole; Raymond H. Myers; Sharon L. Myers; Keying E. Ye
ISBN: 9780321629111

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An ecologist wishes to mark off a circular sampling region