Question

Let 𝑋1, 𝑋2 be a random sample from a 𝑈(0, 𝜃) distribution, where 𝜃>0 is an unknown parameter. For testing the null hypothesis 𝐻0 ∶ 𝜃∈(0,1]∪[2, ∞) against 𝐻1: 𝜃∈(1, 2), consider the critical region
$𝑅={(𝑥_1, 𝑥_2 )∈ℝ × ℝ∶\frac{5}{4}<max\,{𝑥_1, 𝑥_2 }<\frac{7}{4}}.$
Then, the size of the critical region equals____.

Answer 1

The correct answer is: 0.375