The clumsy coupon collector time converges to Gumbel when p=o(1/m), exponential when p=ω(1/m), and a birth-death process when p=c/m.
On a classical problem of probability theory.A Magyar Tudomanyos Akademia Matematikai Kutato Intezetenek k¨ ozlem´ enyei, 6(1-2):215–220
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The clumsy coupon collector's problem
The clumsy coupon collector time converges to Gumbel when p=o(1/m), exponential when p=ω(1/m), and a birth-death process when p=c/m.