The Most Powerful Test with a Leftover Budget

A single observation $X\in\{1,2,3,4,5\}$ has one of two distributions: | x | 1 | 2 | 3 | 4 | 5 | |---|---|---|---|---|---| | $P_0(x)$ | 0.40 | 0.30 | 0.15 | 0.10 | 0.05 | | $P_1(x)$ | 0.10 | 0.20 | 0.30 | 0.15 | 0.25 | Among all tests of $H_0$ (distribution $P_0$) against $H_1$ (distribution $P_1$), including randomized tests, whose size is at most 0.12, what is the largest possible power? Give a decimal or reduced fraction.

• statistics

Source: Neyman-Pearson lemma (1933). Numbers and framing written for AxiomIQ. Statement written for AxiomIQ.