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The known result for the output reading of a quasi-peak detector to periodic pulse inputs is here extended to cover inputs made up of regularly repeated pulses of the same shape, but with random amplitudes. The cosine envelope was chosen for the pulse shape and is viewed as a satisfactory approximation for the typical IF amplifier impulse response. The probability distribution for the pulse amplitude was assumed uniform over an amplitude interval; the latter is a parameter in the analysis so that the result applies, at one extreme, to pulses ranging randomly from zero amplitude to some maximum, and at the other extreme, to fixed amplitude pulses. Solutions are provided for low-frequency inputs-such as would be developed at the output of an IF amplifier followed by an envelope detector, and RF inputs-such as would be found directly at the IF amplifier output.