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.
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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.