B 669 : Part 1 , Sublinear in Space
نویسنده
چکیده
Pr[|X −E[X]| ≥ a] = Pr[(x−E[x]) ≥ a] ≤ E[(x−E[x]) 2] a2 = Var[X] a2 1.3 Example: Coupon Collector Xi : # boxes bought when you have exactly i− 1 different coupons, and after buying these boxes, you have i different coupons. Let X = ∑ i∈nXi: # boxes one bought until at least one of every type of coupon is obtained. Let pi be the probability of obtaining a new coupon when we have exactly i−1 different coupons. pi = 1− i−1 n . Then E[Xi] = 1 pi = n n−i+1 . Therefore E[X] = nHn ≈ n lnn. By Markov, Pr[X ≥ 2n lnn] ≤ 1/2.
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