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The method of Marcum for finding the probability density function associated with a pulsed radar with integration and a square law detector is extended to include the case of a randomly modulated sinusoidal signal. Two mathematical procedures are developed, the well‐known Edgeworth asymptotic series and a convergent series suggested by Varma. Sets of curves are drawn for probability of detection vs average signal‐to‐noise power ratio. Some previous work has shown very high values for probability of detection resulting if it is assumed necessary to detect only one out of many pulses. Such probability levels are reduced if a slowly varying random amplitude of signal is postulated.