A car panel is spray-painted by a machine, and the technicians are particularly interested in the thickness of the resulting paint layer. Suppose that the random variable A measures the thickness of the paint in millimeters at a randomly chosen point on a randomly chosen car panel, and that A" takes values between 0.125 and 0.5 mm with a probability density function of
f(x) = A(0.5-(x-0.25)2)
for 0.125 ≤ x ≤ 0.5 and f(x) = 0 elsewhere.
(a) Find the value of A and sketch the probability density function.
(b) Construct and sketch the cumulative distribution function.
(c) What is the probability that the paint thickness at a particular point is less than 0.2 mm?
(This problem is continued in Problems 2.3.12 and 2.4.7.)