Errors in measuring the arrival time of a wave front from an acoustic source can sometimes be modeled by a beta distribution. (See Perruzzi and Hilliard, J. Acoustical Society of America,1984) Suppose these errors have a beta distribution with a = 1 and β = 2, with measurements in microseconds.
a Find the probability that such a measurement error will be less than 0.5 microseconds.
b Find the mean and standard deviation of these error measurements.