Stochastic Resonance (SR) is a phenomenon that occurs in certain non-linear systems in which noise can be used to improve the system response [L. Gammaitoni, 1998]. A recent approach to quantizer design has employed Stochastic Resonance by randomizing the threshold of the quantizer (Stochastic Thresholding). Stochastic Thresholding has shown a good performance in detection of weak signals buried in heavy noise even in -50 dB SNR. In fact, Stochastic Thresholding helps ML estimation by some Fisher Information gain given in the quantizer. Driven by this motivation, in this paper we obtain new results on Stochastic Resonance in one-bit quantizers. Also, some discussions on threshold Probability Distribution Function (PDF) especially on the relation of the mean and the variance of PDF with a constant signal which we intend to estimate are implemented.