Unformatted text preview: y editors catch errors with unknown probabilities of success
p1 and p2 . Let X0 be the number of typos that neither found. Let X1 and X2
be the number of typos found only by 1 or only by 2, and let X3 be the number
of typos found by both. (a) Find the joint distribution of (X0 , X1 , X2 , X3 ). (b)
Use the answer to (a) to ﬁnd an estimates of p1 , p2 and then of the number of
undiscovered typos.
2.52. A light bulb has a lifetime that is exponential with a mean of 200 days.
When it burns out a janitor replaces it immediately. In addition there is a
handyman who comes at times of a Poisson process at rate .01 and replaces the
bulb as “preventive maintenance.” (a) How often is the bulb replaced? (b) In
the long run what fraction of the replacements are due to failure?
2.53. Starting at some ﬁxed time, which we will call 0 for convenience, satellites
are launched at times of a Poisson process with rate . After an independent
amount of time having distribution function F and mean µ, the...
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This document was uploaded on 03/06/2014 for the course MATH 4740 at Cornell.
 Spring '10
 DURRETT
 The Land

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