In using the triangulation method to determine the range of an acoustic source,

Question

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, measurements errors in these times can be modeled as possessing a uniform distribution from -.05 to +.05 us.
a. What is the probability that a particular arrival-time measurement will be accurate to within .01 us?
b. Find the mean and variance of the measurement errors.

Explanation / Answer

a) probability that a particular arrival-time measurement will be accurate to within .01 us = (0.1 - (-0.1))/ (0.5 - (-0.5))

= 0.2/1 = 0.2

b) Mean of exponential distribution = (a + b)/2

Here a = -0.5, b = 0.5

Mean = (0.5 - 0.5)/2 = 0

Variance = (b - a)^2/12 = (0.5 - (-0.5))2 /12 = 1/12 = 0.0833

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