(Solved): plz solve b and draw a graph carefully 2. Let \( X_{1}, X_{2} \) be iid uniform \( (\theta, \theta+ ...

plz solve b and draw a graph carefully

2. Let \( X_{1}, X_{2} \) be iid uniform \( (\theta, \theta+1) \). For testing \( H_{0}: \theta=0 \) versus \( H_{a}: \theta>0 \), we have two competing tests: test 1: reject \( H_{0} \) if \( X_{1}>0.95 \), test 2: reject \( H_{0} \) if \( X_{1}+X_{2}>C \). (a) Find the value of \( C \) so that test 2 has the same level as test 1. (b) Calculate the power function of each test. Draw a well-labeled graph of each power function. (c) Prove or disprove: test 2 is more powerful than test 1.