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On the coupon-collector's problem with several parallel collections

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arxiv 1609.04174 v1 pith:VO63TASU submitted 2016-09-14 math.PR

classification math.PR
keywords collectionscouponsparallelarrivescasecompletecoupon-collectorequal
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abstract

In this note we evaluate the expectation and variance of the waiting time to complete $m$ parallel collections of coupons, in the case of coupons which arrives independently, one by one and with equal probabilities.

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    The paper formalizes expert caching in MoE LLMs as layered paging, proves near-tight competitive lower bounds, and shows a layer-aware LRU variant beats standard LRU on real traces.

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