Mathematics, 10.03.2020 03:04 keylor97
Let X = the time (in 10β1 weeks) from shipment of a defective product until the customer returns the product. Suppose that the minimum return time is Ξ³ = 3.5 and that the excess X β 3.5 over the minimum has a Weibull distribution with parameters Ξ± = 2 and Ξ² = 2.5.
(a) What is the cdf of X?
F(x) = 0 x < 3.5
1βe^β((xβ3.5)2.5)2 x β₯ 3.5
(b) What are the expected return time and variance of return time? [Hint: First obtain
E(X β 3.5)
and
V(X β 3.5).]
(Round your answers to three decimal places.)
E(X) = 10^β1 weeks
V(X) = (10^β1 weeks)2
c) Compute
P(X > 6).
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