I understand how i should use f1(x)/f0(x) > a/b to solve this problem but am not sure what to use as f1(x) and f0(x) because they are given as piece wise functions. any help?? should i just use 2x and 1 and solve to get x> 1/4?

f0(x)= 1 for x between 0 and 1

0 otherwise

f1(x)= 2x for x between 0 and 1

0 otherwise

Suppose that a single observation X is taken from a distribution for which the pdf f(x) is either f0(x) or f1(x) and the following simple hypothesis are to be tested:

Null: f(x)= f0(x)

Alternative: f(x)= f1(x)

Describe a test procedure for which the value of alpha+2beta is a minimum. And determine the minimum attained by that procedure.