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On a circle of unit circumference arcs of length a are placed at random. Let N α be equal to the necessary number of arcs to cover at least the length 1 − p , 0 ≦ p 1, of the circumference at least m (≧1) times. In the present paper limit distributions of N α are derived when α → 0. Some results for spacings are also obtained.
Lars Holst (Sat,) studied this question.
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