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A method is outlined for estimating the probability of detection for a pulsed radar, assuming a randomly modulated carrier. For a square law detector closed forms for the moments of the distribution of the envelope are presented in terms of three different choices of the distribution of carrier amplitude, thus leading to an Edgeworth series representation of the desired probability. At least one choice of distribution of the carrier amplitude leads to closed forms for the moments for the case of a linear detector. Curves of probability of detection vs signal‐to‐noise power ratio are constructed and cross checked by a method of numerical integration.