• Journal of the Korean Data and Information Science Society
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• v.27 no.5
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• pp.1241-1251
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• 2016

We consider a correlated discrete-time random walk in which the current jump size depends on the previous jump size and a noncorrelated discrete-time random walk where the jump size is determined independently. By using the strong law of large numbers of Markov chains we derive the formula for the asymptotic means of the random mixture and the periodic pattern of these two random walks and then we show that there exists Parrondo's paradox where each random walk has mean 0 but their random mixture and periodic pattern have negative or positive means. We describe the parameter sets at which Parrondo's paradox holds in each case.

• Honam Mathematical Journal
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• v.30 no.2
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• pp.311-321
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• 2008

Mathematical paradoxes may arise when computations give unexpected results. We use three paradoxes to illustrate how they work in the basic probability theory. In the process of resolving the paradoxes, we expect that student-teachers can pedagogically gain valuable experience in regards to sharpening their mathematical knowledge and critical reasoning.