A randomised Neyman–Pearson test: reject at $x=4$ with probability $0.2$

The distributions of X under $H_0$ and $H_1$ are given by:

$$\begin{array}{c|cccc} x & 1 & 2 & 3 & 4\\\hline H_0 & 0.25 & 0.25 & 0.25 & 0.25\\ H_1 & 0.17 & 0.17 & 0.17 & 0.32 \end{array}$$

The most powerful test at level $\alpha=0.05$ is given by: