魏慶榮臺灣大學：數學研究所黃佳慧Huang, Chia-HuiChia-HuiHuang2007-11-282018-06-282007-11-282018-06-282004http://ntur.lib.ntu.edu.tw//handle/246246/59424Suppose that we have two biased coins with probability of getting head p1 and p2, respectively, where (p1-1/2)(p2-1/2)<0. We are interested in devising an algorithm to generate a Bernoulli random variable with probability of getting head is 1/2. This question is motivated by the challenge question on getting a perfect lottery machine through non-perfect lottery machines. We propose a sequential adaptive algorithm on flipping the just-described two coins to generate a Bernoulli random variable with probability of getting head is 1/2. The asymptotic properties of this algorithm will be presented. The performance of this approximation is much better than that of the algorithm based on classical stochastic approximation in which the structure of this particular problem is not fully utilized. In addition, we use a simulation study to demonstrate that the asymptotic approximation is reasonable well with moderate sample size.1 Intriduction----------------------2 2 Stochastic Approximatiomn---------5 3 Proposed Algorithm----------------11 4 Main Results----------------------19 Reference---------------------------42217676 bytesapplication/pdfen-US隨機逼近鞅論stochastic approximationmartingalethesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/59424/1/ntu-93-R90221019-1.pdf