In clinical interpretations radiologists do not know the location of lesions that may be present in the images, and they differ in their abilities to search images and find lesions. The receiver operating characteristic (ROC) model does not directly model the search ability of the observer. The aims of this work were (a) to present a simplified model that includes a search parameter, and (b) describe an algorithm for estimating the parameters of the model from free-response receiver operating characteristic (FROC) data. The model consists of two unit-variance normal distributions, noise and signal, separated by mu. The lesion decision variable (DV) samples are generated by sampling the signal distribution s times, where s is the known number of lesions in the image. The noise DV samples are generated by sampling the noise distribution n times, where n is the unknown number of noise sites in the image. The model regards n as an integer random variable that is realized by sampling a Poisson distribution with intensity parameter lambda. Under the assumption that all DV samples are independent, a maximum likelihood method succeeded in estimating the population values of the parameters from simulated FROC data. The ROC curves predicted by the model are "proper", i.e., they do not cross the chance diagonal. The model also predicts the widely observed result in ROC studies that the noise distribution is narrower than the signal distribution, corresponding to b < 1 in the familiar ROC model.