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Compute the expected value of the total amplitude

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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.

Reference no: EM13985431

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