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(c) Suppose Vi, i = 1,. . .,n, are independent exponential random variables with rate 1. Denote n X=rnax{n:Zl/,;A}, i=1 so X can be thought

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(c) Suppose Vi, i = 1,. . .,n, are independent exponential random variables with rate 1. Denote n X=rnax{n:Zl/,;A}, i=1 so X can be thought of as being the maximum number of exponentials having rate 1 that can be summed and still be Items than or equal to A. (i) Using properties of a Poisson process with rate 1, explain Why X has a Poisson distibution with parameter A

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