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Suppose that 2000 points are selected independently and at

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

Solution for problem 7E Chapter 2.4

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 7E

Suppose that 2000 points are selected independently and at random from the unit square {(x, y) : 0 ≤ x < 1, 0 ≤ y < 1}. Let W equal the number of points that fall into A = {(x, y) : x2 + y2 < 1}.

(a) How is W distributed?

(b) Give the mean, variance, and standard deviation ofW.

(c) What is the expected value of W/500?

(d) Use the computer to select 2000 pairs of random numbers. Determine the value of W and use that value to find an estimate for π. (Of course, we know the real value of π, and more will be said about estimation later in this text.)

(e) How could you extend part (d) to estimate the volume V = (4/3)π of a ball of radius 1 in 3-space?

(f) How could you extend these techniques to estimate the “volume” of a ball of radius 1 in n-space?

Step-by-Step Solution:

Answer

Step 1 of 8

The condition is x2+y2<1

P is the point lie in the shaded region

p=


Step 2 of 8

Chapter 2.4, Problem 7E is Solved
Step 3 of 8

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: estimate, radius, could, random, space. This expansive textbook survival guide covers 59 chapters, and 1476 solutions. The full step-by-step solution to problem: 7E from chapter: 2.4 was answered by , our top Statistics solution expert on 07/05/17, 04:50AM. This textbook survival guide was created for the textbook: Probability and Statistical Inference , edition: 9. The answer to “Suppose that 2000 points are selected independently and at random from the unit square {(x, y) : 0 ? x < 1, 0 ? y < 1}. Let W equal the number of points that fall into A = {(x, y) : x2 + y2 < 1}.(a) How is W distributed?(b) Give the mean, variance, and standard deviation ofW.(c) What is the expected value of W/500?(d) Use the computer to select 2000 pairs of random numbers. Determine the value of W and use that value to find an estimate for ?. (Of course, we know the real value of ?, and more will be said about estimation later in this text.)(e) How could you extend part (d) to estimate the volume V = (4/3)? of a ball of radius 1 in 3-space?(f) How could you extend these techniques to estimate the “volume” of a ball of radius 1 in n-space?” is broken down into a number of easy to follow steps, and 150 words. Since the solution to 7E from 2.4 chapter was answered, more than 546 students have viewed the full step-by-step answer. Probability and Statistical Inference was written by and is associated to the ISBN: 9780321923271.

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Suppose that 2000 points are selected independently and at