Stochastic

Suppose that n1 0 3 and n2 0 1 a what is the

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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.

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