This paper presents a frequency-domain technique for estimating distributed lag coefficients (the impulse-response function) when observations are randomly missed. The technique treats stationary processes with randomly missed observations as amplitude-modulated processes and estimates the transfer function accordingly. Estimates of the lag coefficients are obtained by taking the inverse transform of the estimated transfer function. Results with artificially created data show that the technique performs well even when the probability of an observation being missed is one-half and in some cases when the probability is as low as one-fifth. The approximate asymptotic variance of the estimator is also calculated in the paper.