# In order to have a simple metaphor with which to

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Unformatted text preview: satellite stops working. Let X (t) be the number of working satellites at time t. (a) Find the distribution of X (t). (b) Let t ! 1 in (a) to show that the limiting distribution is Poisson( µ). 2.54. Calls originate from Dryden according to a rate 12 Poisson process. 3/4 are local and 1/4 are long distance. Local calls last an average of 10 minutes, while long distance calls last an average of 5 minutes. Let M be the number of local calls and N the number of long distance calls in equilibrium. Find the distribution of (M, N ). what is the number of people on the line. 2.55. Ignoring the fact that the bar exam is only given twice a year, let us suppose that new lawyers arrive in Los Angeles according to a Poisson process with mean 300 per year. Suppose that each lawyer independently practices for an amount of time T with a distribution function F (t) = P (T t) that has F (0) = 0 and mean 25 years. Show that in the long run the number of lawyers in Los Angeles is Poisson with mean 7500. 2.6. EXER...
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## This document was uploaded on 03/06/2014 for the course MATH 4740 at Cornell University (Engineering School).

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