Let X = the time (in 10-1 weeks) from shipment of a defective product until the customer returns the product. Suppose that the minimum return time is ϒ = 3.5 and that the excess X – 3.5 over the minimum has a Weibull distribution with parameters α = 2 and β = 1.5 see “Practical Applications of the Weibull Distribution,” Industrial Quality Control, Aug. 1964: 71–78).
a. What is the cdf of X?
b. What are the expected return time and variance of return time? [Hint: First obtain E(X – 3.5 )and V(X – 3.5).]
c. Compute P(X > 5).
d. Compute P(5 ≤ X ≤ 8).
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