Let X have the following hypothetical distribution:
$H_0 : P(X=0)=P(X=1/2)=P(X=1)=1/3$
$H_1$: $X$ is continuous and uniform on $[0,1]$.
I am supposed to find the Most Powerful test for testing $H_0$ against $H_1$ at level $\alpha=0.05.$
I know the theory about the MPT theory but since I am new to this, I wasn't able to apply it on the question. Please help.