Suppose Xn,1,..., Xn,n are i.i.d. Bernoulli trials with success probability pn. If pn p (0,

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Suppose Xn,1,..., Xn,n are i.i.d. Bernoulli trials with success probability pn. If pn → p ∈ (0, 1), show that n1/2

[X¯ n − pn] d

→ N(0, p(1 − p)) .

Is the result true even if p is 0 or 1?

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Testing Statistical Hypotheses Volume I

ISBN: 9783030705770

4th Edition

Authors: E.L. Lehmann, Joseph P. Romano

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Question Posted: Nov 04, 2024 04:00 AM

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Suppose Xn,1,..., Xn,n are i.i.d. Bernoulli trials with success probability pn. If pn p (0,

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Testing Statistical Hypotheses Volume I

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