We look at estimation of the probability density function when the sample observations are randomly censored. The kernel density estimator that is based on the Kaplan-Meier product limit estimator is well-accepted for this problem. However, the construction of this estimator requires a smoothing parameter or bandwidth. We propose a data-driven bandwidth selection procedure that is an extension of the Discrepancy Principle in the case of random samples. We also give a new interpretation to the kernel density estimator. We show that this is the solution to a smoothed modified likelihood problem. This new interpretation serves as the motivation for the proposed EM algorithm, we call NEMS algorithm, for estimating the probability density function when observations are randomly censored. Like the kernel density estimator, what we propose also requires a bandwidth or smoothing parameter. For this, we investigate the applicability of the Discrepancy Principle.