Question: 6. (a) Let 0 < a < 1 and Tn = X k: |k1 2 n|>1 2 an n k . By considering

6.

(a) Let 0 < a < 1 and Tn =

X k: |k−1 2 n|>1 2 an



n k



.

By considering the binomial distribution or otherwise, show that T

1/n n →

2 p

(1 + a)1+a(1 − a)1−a

.

(b) Find the asymptotic behaviour of T 1/n n , where a > 0 and Tn =

X k: k>n(1+a)

nk k!

.

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