- 4 2 3 Use Example 10 25 To Answer The Following Questions Let X1 X2 Xdenote A Random Sample From The Expone 1 (91.88 KiB) Viewed 21 times
(4) (2) 3. Use Example 10:25 to answer the following questions. Let X1, X2, ..., Xdenote a random sample from the exponential density with mean 6, and let Y , Y2, ..., Y, denote an independent random sample from an exponential density with mean 8. a Find the likelihood ratio criterion for testing H,:6, = 8, versus H,:6, 6 12. For question a: Answer the questions as a stepwise solution. 3.1. Find the MLE of 2 (same result will apply to 01). 3.2. Find L(12) = L(0,02). 3.3. Find the likelihood function () in the unrestricted space. 3.4. Find the likelihood function (120) = L(0) in the restricted space. 3.5. Find the MLE of e. 3.6. Substitute the MLE of 0 into likelihood function of the estimated restricted space. 3.7. Find the likelihood ratio test 1. 3.8. Use the following to find to do a hypothesis test using Theorem 10.2 when 100, n = 200,X = 1 and Y = 1.5 and a = 0.1. (2) (2) (3) (2) m = = (4)