QZ 3-C - probability that the seventh time the laptop needs...

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STAT 400 Fall 2011 Version C Name ANSWERS . Quiz 3 (10 points) Be sure to show all your work; your partial credit might depend on it. No credit will be given without supporting work. 1. Alex purchased a laptop computer at Joe’s Discount Store . He also purchased “Lucky 7” warranty plan that would replace the laptop at no cost if it needs 7 or more repairs in 3 years. Suppose the laptop requires repairs according to Poisson process with the average rate of one repair per 4 month. X t = number of repairs in t years. Poisson ( λ t ) T k = time of the k th repair. Gamma, α = k . one repair per 4 month λ = 3. a) (4) Find the probability that the laptop would not need to be replaced. That is, find the
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Unformatted text preview: probability that the seventh time the laptop needs repair will be after 3 years, when the warranty expires. P ( T 7 > 3 ) = P ( X 3 ≤ 6 ) = P ( Poisson ( 9 ) ≤ 6 ) = 0.207 . OR P ( T 7 > 3 ) = ( ) ∫ ∞ Γ--3 3 1 7 7 7 3 dt t t e = ∫ ∞-3 3 6 7 6 3 ! dt t t e = … b) (6) Find the probability that the seventh time the laptop needs repair will be during the second year of warranty. P ( 1 < T 7 < 2 ) = P ( T 7 > 1 ) – P ( T 7 > 2 ) = P ( X 1 ≤ 6 ) – P ( X 2 ≤ 6 ) = P ( Poisson ( 3 ) ≤ 6 ) – P ( Poisson ( 6 ) ≤ 6 ) = 0.966 – 0.606 = 0.360 . OR P ( 1 < T 7 < 2 ) = ( ) ∫--Γ 2 1 3 1 7 7 7 3 dt t t e = ∫-2 1 3 6 7 6 3 ! dt t t e = …...
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