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In using the triangulation method to determine the range
Chapter 4, Problem 54E(choose chapter or problem)
Problem 54E
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.
Questions & Answers
QUESTION:
Problem 54E
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.
ANSWER:
Solution:
Step 1 of 2:
We have the Uniform distribution with the interval -0.05 to 0.05
Le X follows the Uniform distribution with density
f(x) =
-
The claim is to find the probability that particular arrival-time measurement will be accurate to within 0.01
We have a = -0.05 and b = 0.05
Then, f(x) =
X = amount of measurement error, X is Uniform on the interval
P(-0.02 < X < 0.05) = dx
=
xdx
= [ x
=
Hence, the probability that particular arrival-time measurement will be accurate to within 0.01 is