Consider again the plastic bending capabilities discussed in Problem 2.2.8. What is the expected deformity angle? What is the median deformity angle?
Problem 2.2.8
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 0o and 10o with a probability density function
f(θ) = A(el0-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.)