Question: 3. (25 marks) Suppose X = (X1, ..., X,) is a random sample from Exponential(0) with proba- bility density function f(x) = de-x, x >

3. (25 marks) Suppose X = (X1, ..., X,) is a random sample from Exponential(0) with proba- bility density function f(x) = de-x, x > 0. Consider test Ho : 0 = 00 versus H1 : 0 # 00. (a) (8 marks) Find the likelihood ratio 1(X). (b) (8 marks) Based on part (a), construct the likelihood ratio test and find the critical region at the significance level a. (c) (9 marks) Consider a one-side test Ho : 0 = 0% versus H, : 0 > 60. Construct the likelihood ratio test and find the critical region at the significance level a

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