Abstract: As mathematical fundamental of stochastic computing system, transfer function of variance and expected value based on Bernoulli distribution is not accurate and general in system analysis. A novel mathematic method, hypergeometric decomposition is proposed to solve this problem; it offers a general way to calculate transfer function of expected value and variance under more complicated circumstance. There are four groups of transfer function proposed here, which proves the effectiveness of stochastic computing system in a more general way; also they offer a better way to evaluate stochastic system. Compared with traditional bit-level simulation, evaluation method based on variance is time saving, accurate and comprehensive. New variance transfer function includes type of input random stream into performance analysis for the first time, which proves that specific length of stochastic sequence can maximize system performance.