*16. The following problem arises in molecular biology. The surface of a bacterium consists of several sites...
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*16. The following problem arises in molecular biology. The surface of a bacterium consists of several sites at which foreign molecules
—some acceptable and some not—become attached. We consider a particular site and assume that molecules arrive at the site according to a Poisson process with parameter λ. Among these molecules a proportion α is acceptable. Unacceptable molecules stay at the site for a length of time that is exponentially distributed with parameter , whereas an acceptable molecule remains at the site for an exponential time with rate . An arriving molecule will become attached only if the site is free of other molecules. What percentage of time is the site occupied with an acceptable
(unacceptable) molecule?
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