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.

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)