The probability density function for the diameter of a drilled hole in a metal shop plant is 10e^[-10(x-5)] for x > 5mm. Although the target diameter is 5 millimeters, vibrations, tool wear, and other nuisances produce diameters larger than 5 millimeters.
a.Determine the mean and variance of the diameter of the holes.
b.Determine the probability that a diameter exceeds 5.1 millimeters.