Consider two probability density functions on [0,1]:$f_0(x) = 1$, and $f_1(x) = 2x$. Among all the tests of the null hypothesis $H_0 : X \sim f_0(x)$ versus the alternative $X \sim f_1(x)$, with a significance level $\alpha$ = 0.10. How large can the power possibly be?
Now I know the power of a test equals the probability of not making a type II error (accept a false null hypothesis). But I have no idea how to find the power in this scenario? Any ideas?