7. Assume that X₁,..., Xn is a random sample from a Bernoulli (p) and let Yn n 1/1 X₁. For p # 1/2, Determine the asymptotic distribution of √n[Yn(1 – Yn) - p(1 - p)].

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7. Assume that X₁,..., Xn is a random sample from a Bernoulli (p) and let Yn n 1/1 X₁. For p # 1/2, Determine the asymptotic distribution of √n[Yn(1 – Yn) - p(1 - p)].

 

 

7. Assume that \( X_1, ..., X_n \) is a random sample from a Bernoulli(p) and let \( {Y}_n = \1/n\sum_{i=1}^{n} X_i \). For \( p =/ 1/2), Determine the asymptotic distribution of \( \sqrt{n}({Y}_n(1 - {Y}_n) - p(1 - p))  \).

7. Assume that X₁, Xn is a random sample from a Bernoulli(p) and let Y₁ =
EX. For p # 1/2, Determine the asymptotic distribution of √Y (1-
Yn)-p(1-p)].
71
Transcribed Image Text:7. Assume that X₁, Xn is a random sample from a Bernoulli(p) and let Y₁ = EX. For p # 1/2, Determine the asymptotic distribution of √Y (1- Yn)-p(1-p)]. 71
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