In determining the range of an acoustic source by triangulation, one must accurately measure the time at which the spherical wave front arrives at a receiving sensor. According to Perruzzi and Hilliard (1984), errors in measuring these arrival times can be modeled as having uniform distributions. Suppose that measurement errors are uniformly distributed from?0.04 to+0.05 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 the variance of these measurement errors.
If we have a random variable X with mean µ, are P(X ? µ) and P(X ? µ) necessarily 50%? Can you give an example where this doesn't happen? Where it does happen?