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Q103Section III (Statistics)103 of 145

n(2Xˉ−θ)⟶dN(0,θ2/3)\sqrt n(2\bar X-\theta)\overset{d}{\longrightarrow} N(0,\theta^2/3), so the square is θ2χ12/3\theta^2\chi^2_1/3

Let X1,…,XnX_1,\dots,X_n be a random sample from U(0,θ)U(0,\theta). Then the asymptotic distribution of 3n(2Xˉ−θ)23n(2\bar X-\theta)^2 is:

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