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In certain cases, noises can improve signal transmission or signal processing. This phenomenon is the so-called stochastic resonance. In this paper, we firstly present two theorems to prove that the noisy threshold neuron shows stochastic resonance in terms of the probability of correct reception. Secondly, we analytically discuss stochastic resonance effects and give the probability-optimal noise levels for four representative noises. Finally, we discuss the stochastic gradient ascent learning law, which can be used to find the probability-optimal noise levels. We also present our simulation results for the four representative noises. These results indicate that stochastic resonance is favorable both in biological neurons and in signal processing.