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

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

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 ) = ( ) --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 ) = ( ) -- 2 1 3 1 7 7 7 3 dt t t e = -2 1 3 6 7 6 3 ! dt t t e =...
View Full Document

Ask a homework question - tutors are online