Neyman-Pearson Most Powerful Test (Size 0.04 & 0.10)|UPSC IFoS 2025 Statistics Paper 1|Problem-1(e) скачать в хорошем качестве

Neyman-Pearson Most Powerful Test (Size 0.04 & 0.10)|UPSC IFoS 2025 Statistics Paper 1|Problem-1(e)

Complete *Question 1 Part 5* from **UPSC Indian Forest Service 2025 Statistics Optional Paper 1**! Using **Neyman-Pearson Lemma**, we construct: **Most Powerful Test of size α = 0.04**: Reject \( H_0 \) if \( X \in \{1,2,3,4\} \) (exact size 0.04). Type II error β = 0.82. **Most Powerful Test of size α = 0.10**: Reject \( H_0 \) if \( X \in \{1,2,3,4,5,6\} \) or if \( X=7 \) with probability \( \gamma = \frac{2}{47} \approx 0.0425 \). Power = 0.2436. Master *Likelihood Ratio Tests**, **randomized tests**, and **power calculations* for discrete distributions! #UPSC #UPSCIFS #IndianForestService #UPSCStatisticsOptional #UPSC2025 #NeymanPearson #MostPowerfulTest #LikelihoodRatioTest #HypothesisTesting #TypeIIError #PowerOfTest #StatisticsForUPSC #IndianStatisticalService #UPSCPreparation #ForestServiceExam #UPSCOptionalStatistics #UPSCForestService #ExamPreparation #CompetitiveExams