Statistical inference - likelihood ratio test

Please answer this question below.

Thank you!

(Hint: The null hypothesis is also same as H₀ : ??1?? = ??2?? vs H_a : ??1??=?2?? ).

Let X] and X2 follow independent exponential distributions with parameters 61 and 02, respectively. Define 0 = 01/02. We would like to test Ho : 0 = 1 against H1 : 0 # 1. (a) Show that the likelihood ratio statistic is 4F/(1 + F)', where F = X2/ X1. (b) Derive the rejection region for a size o likelihood ratio test