文章基本信息

标题：One Bulb? Two Bulbs? How Many Bulbs Light Up? -- A Discrete Probability Problem Involving Dermal Patches
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作者：C. Radhakrishna Rao ; Pennsylvania State University ; University Park 等
期刊名称：Sankhya. Series A, mathematical statistics and probability
印刷版ISSN：0976-836X
电子版ISSN：0976-8378
出版年度：2007
卷号：69
期号：02
出版社：Indian Statistical Institute
摘要：A dermal patch is designed to activate some targeted receptors. On Day 1, the patch releases one dose of medicine, which latches onto a receptor and makes it active. On Day 2, the patch releases two doses of medicine, which latch onto two receptors, one dose per receptor. If the receptor is already active, the new dose makes it inactive. If the receptor is inactive, the new dose makes it active. On Day 3, the patch releases three doses of medicine, which latch onto three receptors, one dose per receptor. This continues for ten days with the patch releasing a total of 55 doses progressively. In this paper, we obtain the distribution of the number of receptors active at the end of Day 10.
关键词：Asymptotic normality, clubbed binomial distribution, de Finetti's theorem, discrete probability, exchangeability, modulo operation, two-element compact group.