Let X1 , ... , Xn ∼ Uniform(0, θ) and let Y = max{X1 , ... , Xn }. We want
to test H0 : θ = 1/2 versus H1 : θ > 1/2.

Suppose we decide to test this hypothesis by rejecting H0 when Y > c. Find the power function.

B(θ) = P ( Y is in the rejection region)
= P ( Y > c)
= P (max{X1 , ... , Xn } > c)
= 1 - P (max{X1 , ... , Xn } < c)
= 1 - [P(Xi < c)]^n


Okay, so where I start to go wrong is finding P(Xi < c). Given that it's uniform, should it just be C/θ? I have written down in my previous notes the answer is min{C, θ}/θ

I'm trying to draw a picture to figure out how this is the case. Can anyone help? Cheers!