Question: Problem 3. Let Yn Bin(n, p) with p (0, 1). (i) Derive the CLT for Yn/n. (ii) Derive the CLT for log(1 + Yn/n ).

Problem 3. Let Yn Bin(n, p) with p (0, 1).

(i) Derive the CLT for Yn/n.

(ii) Derive the CLT for log(1 + Yn/n ).

(iii) Set log 0 = 0. Do we have the same CLT as in (ii) if log(1 + Yn/ n ) is replaced by log Yn /n ? Show your work.

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