Abstract: Based on the theory of “sum of random variables” distribution, the author has put forward a new idea(“sum of random variables”) for the sensitive issues survey, designed a corresponding model (response model of “sum of random variables”), and realized the questionnaire survey of sensitive issues, therefore further improved the confidential of the sensitive issues survey. The optimal model estimation and variance calculation are given, the reasonable choice of the model parameters is discussed, and other results and case calculation are further discussed.