6.22 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 arrivaltime measurement will be in error by less than 0.01 microsecond.

b Find the mean and variance of these measurement errors.