Suppose that electrical pulses having iid random amplitudes, Ask an Expert

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Suppose that electrical pulses having i.i.d. random amplitudes A1, A2, . . . arrive at a counter in accordance with a Poisson process with intensity λ. The amplitude of a pulse is assumed to decrease exponentially, that is, if a pulse has amplitude A upon its arrival, then its amplitude at time t is Ae-αt, where α is some positive parameter. We finally assume that the initial amplitudes of the pulses are independent of the Poisson process. Compute the expected value of the total amplitude at time t.

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Statistics and Probability, Statistics

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