CoursHeroTranscribedText: 1. 1 ... . ~ (0, ) (1) Find CRLB(Cramer Rao Lower Bound) (2) Show that variance of [(n + 1)/n] is less than CRLB and explain. 2. ~ , = = 0 = exp (). (1) Is exp unbiased estimator for ? (2) Find the MSE of exp 3. Suppose that 1 ... . ~ 1 , 2 1 < < 2 . (1) Show that (1) , () are complete sufficient statistics. (2) Find MVUE for (1 + 2 )/2 4. Show that (, 2 ) hasn't completeness (when, 1 ... . ~ , 2 ) 5. 1 ... . ; = exp ( > 0, > 0 ) (1) Find 90% confidence interval for 2 . (2) Find 90% confidence interval for exp = ( > 1). 6. 1 ... . ; = 1 + 0 1 , > 0 and 0 = 0 1 > 0 then, (1) find most powerful test. (2) Is The result of (1) can be uniformly most powerful test ? 7. 1 ... . ; = exp and 0 = 0 1 > 0 then, find appropriate test procedure and explain that whether the test method is uniformly most powerful test or not. exp 8. 1 ... . ; = = 0, 1,2, ... and ! 0 = 10 1 = 11 (1) Find the most powerful test. (2) Find power(1 ) by using normal distribution. 1 9. 1 , 2 are random samples from pdf : ; = exp > 0 . Let 0 = 2 1 = 1 and reject region is 1; 2 2; 2 1 < then, what is ( 1 = 1) ? 1; 1 2; 1 2