The bending capabilities of plastic sheets are investigated by bending sheets at increasingly large angles until a deformity appears in the sheet The angle at which the deformity first appears is then recorded Suppose that this angle takes values between 0o and 10o with a probability density functi...

The bending capabilities of plastic sheets are investigated by bending sheets at increasingly large angles until a

Question:

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 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.)
Distribution
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