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Unformatted text preview: var ( N n ) = n 2 n1 X k =1 1 /k 2n n1 X k =1 1 /k ≤ n 2 ∞ X k =1 1 /k 2 , the righthand side of (*) converges to 0 and ( N nEN n ) / ( nlnn ) converges to 0 in probability. On the other hand, we know E ( N n ) nln = ∑ n k =1 1 /k lnn → 1 , as n → ∞ . Therefore, N n / ( nln ) converges to 1 in probability....
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This note was uploaded on 09/22/2010 for the course MATH 413 at Cornell.
 '08
 PROTSAK
 Probability

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