Let X be a random variable having the exponential distribution

Let X be a random variable having the exponential distribution With parameter A1 and let Y be an independent random variable having the exponential distribution with parameter A2. Note that {X} and {Y} are independent samples each of size 1. 1. Derive the likelihood ratio statistic A for testing H0 : A1 = A2 versus H1 : A1 75 A2. 2. For the likelihood ratio test which rejects H0 for small values of A, deduce that the rejection region is of the form {X / Y > c} U {Y/X > c}. 3. What are the null distributions of X / Y and Y/ X ? 4. Explain how you would select the constant 0 given in part (ii) so that the likelihood ratio test has signicance level a