In determining the range of an acoustic source by triangulation, the time at which the spherical wave front arrives at a receiving sensor must be measured accurately. According to an article by J. Perruzzi and E. Hilliard (Journal of the Acoustical Society of America, 75(1), 1984, pp. 197-201), measurement errors in these times can be modeled as having uniform distributions. Suppose measurement errors are uniformly distributed from to microsecond.
a Find the probability that a particular arrival time measurement will be in error by less than 0.01 microsecond.
b Find the mean and variance of these measurement errors.