# QZ 3-D - probability that the seventh time the laptop needs...

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STAT 400 Fall 2011 Version D 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 6 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 6 month λ = 2. 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 ( 6 ) ≤ 6 ) = 0.606 . OR P ( T 7 > 3 ) = ( ) ∫ ∞ Γ--3 2 1 7 7 7 2 dt t t e = ∫ ∞-3 2 6 7 6 2 ! 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 ( 2 ) ≤ 6 ) – P ( Poisson ( 4 ) ≤ 6 ) = 0.995 – 0.889 = 0.106 . OR P ( 1 < T 7 < 2 ) = ( ) ∫--Γ 2 1 2 1 7 7 7 2 dt t t e = ∫-2 1 2 6 7 6 2 ! dt t t e = …...
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## This note was uploaded on 02/15/2012 for the course STAT 400 taught by Professor Kim during the Spring '08 term at University of Illinois, Urbana Champaign.

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