An iid sample of size 18 has density 2x exp(−x²/θ)/θ on x>0,zero otherwise. Let T=Σx_i²,and let χ²_(α,ν) denote the upper-tail α quantile. Which is a 98% confidence interval for θ?
Transform Y_i=X_i²;these are exponential with mean θ. Thus 2ΣY_i/θ∼χ²₃₆. Place this pivot between its lower .01 and upper .01 quantiles,an event of probability .98,and invert positive inequalities. This gives **A** with the specified upper-tail notation.
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