The number of arrivals N at a supermarket checkout counter in the time interval from 0

Chapter 4, Problem 4.168

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The number of arrivals N at a supermarket checkout counter in the time interval from 0 to t follows a Poisson distribution with mean t. Let T denote the length of time until the first arrival. Find the density function for T . [Note: P(T > t0) = P(N = 0 at t = t0).]

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