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Refer to Exercise 4.54. Suppose that measurement errors

Mathematical Statistics with Applications | 7th Edition | ISBN: 9780495110811 | Authors: Dennis Wackerly; William Mendenhall; Richard L. Scheaffer ISBN: 9780495110811 47

Solution for problem 55E Chapter 4

Mathematical Statistics with Applications | 7th Edition

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Mathematical Statistics with Applications | 7th Edition | ISBN: 9780495110811 | Authors: Dennis Wackerly; William Mendenhall; Richard L. Scheaffer

Mathematical Statistics with Applications | 7th Edition

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Problem 55E

Problem 55E

Refer to Exercise 4.54. Suppose that measurement errors are uniformly distributed between −0.02 to +0.05 μs.

a What is the probability that a particular arrival-time measurement will be accurate to within 0.01 μs?

b Find the mean and variance of the measurement errors.

Reference

In using the triangulation method to determine the range of an acoustic source, the test equipment must accurately measure the time at which the spherical wave front arrives at a receiving sensor. According to Perruzzi and Hilliard (1984), measurement errors in these times can be modeled as possessing a uniform distribution from −0.05 to +0.05 μs (microseconds).

a What is the probability that a particular arrival-time measurement will be accurate to within 0.01 μs?

b Find the mean and variance of the measurement errors.

Step-by-Step Solution:

Solution:

Step 1 of 2:

   Suppose that measurement errors are uniformly distributed between -0.02 to +0.05

a). To find the probability that a particular arrival-time measurement will be accurate to within 0.01 μs.

      Let Y denote the amount of measurement error.

Then Y is uniform on the interval (-0.02, 0.05)

 

Step 2 of 2

Chapter 4, Problem 55E is Solved
Textbook: Mathematical Statistics with Applications
Edition: 7
Author: Dennis Wackerly; William Mendenhall; Richard L. Scheaffer
ISBN: 9780495110811

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Refer to Exercise 4.54. Suppose that measurement errors