Abstract: In engineering the density functions of normal, gamma and beta distributions are often used to fit other pdf f(x). The way to do it is to determine the two parameters in those distributions mentioned above by the first two moments. From the fact that the eigenfunctions of Sturm-Liouville equation form complete orthogonal series, it is shown here that the method usually used just makes the first two generalized Fourier coefficients of the orthogonal expansion of f(x) with respect to the orthogonal series equal to zero.