Question: 1. (25 marks) Let X1, X2, ..., Xn be a random sample from Uniform(01, 02) where 0, and 62 are unknown parameters. Let X(1), ...,

1. (25 marks) Let X1, X2, ..., Xn be a random sample from Uniform(01, 02) where 0, and 62 are unknown parameters. Let X(1), ..., X(x) denote the order statistics of X1, X2, ..., X, . (a) (5 marks) Find the MLE of 6, and 02. (b) (5 marks) Find the probability density function of X(m) and X(1), respectively. (c) (5 marks) Find E(X(m)) and E(X(1)). (d) (5 marks) Find the sufficient statistics for 0, and 02. Are they complete? Please provide detailed steps for your argument. (e) (5 marks) Find the UMVUE of te Hints: The joint probability density function of X() and X() for 1 Si

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