A comparative study between parametric and non-parametric estimation for the probability density function (pdf) is done. The parametric method depends on additional information (or assumptions) about the form of the pdf. A comparison between the two estimates is done using two measures of efficiency, namely, the mean superior of absolute error and the Mean Integrated Square Error (MISE). The Maximum Likelihood (ML) Method and the Kernel method are used to obtain an estimate of the pdf of the normal distribution. The Gaussian and Epanechinkov Kernels are used in the non-parametric case. Although the best conditions of non-parametric estimation are applied, the results showed that the parametric method of exam estimation reduces the approximate MISE of the estimator to 42% (or less) of that of the non-parametric method. The relative efficiency of ML estimator improves with any increase in the sample size. The estimator will be more efficient in the case of one unknow parameter.