The bending capabilities of plastic sheets are investigated by bending sheets at increasingly large angles until a deformity appears in the sheet. The angle θ at which the deformity first appears is then recorded. Suppose that this angle takes values between 0◦ and 10◦ with a probability density function f (θ) = A(e10−θ − 1) for 0 ≤ θ ≤ 10 and f (θ) = 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 a plastic sheet can be bent up to an angle of 8◦ without deforming? (This problem is continued in Problems 2.3.13 and 2.4.8.)