The Borel-Cantelli Lemmas, and Their Relationship to Limit Superior and Limit Inferior of Sets (or, Can a Monkey Really Type Hamlet?)
The purpose of this chapter is to show that if a monkey types infinitely, Shakespeare’s Hamlet and any other works one may wish to add to the list will each be typed, not once, not twice, but infinitely often with a probability of 1. This dramatic fact is a simple consequence of the Borel-Cantelli lemma and will come as no surprise to anyone who has taken a graduate-level course in Probability. The proof of this result, however, is quite accessible to anyone who has but a rudimentary understanding of the concept of independence, together with the notion of limit superior and limit inferior of a sequence of sets.
1983 ◽
Vol 26
(4)
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pp. 516-524
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2016 ◽
Vol 1
(13)
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pp. 104-112
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1996 ◽
Vol 23
(1)
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pp. 89-116
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