From one observation x,test standard normal density exp(−y²/2)/√(2π) against Laplace density exp(−|y|)/2. Which most-powerful rejection region has the correct form?
The alternative/null likelihood ratio is √(2π)/2·exp(x²/2−|x|)=constant·exp[(|x|−1)²/2]. Neyman–Pearson rejects for a large ratio,hence for large ||x|−1|. **C**.
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