Suppose we have X1, X2, X, which are i.i.d. and come from the uniform distribution Uniform(+)...

  

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Suppose we have X1, X2, X, which are i.i.d. and come from the uniform distribution Uniform(+) > 0; 0 = (m) (a) Use the Method of Moments to estimate and 1. (b) Determine whether the estimate derived by the Method of Moments is biased for . (c) Use the Maximum Likelihood method to estimate X(1) = min(X1, X2,..., Xn) and X(n) = max(X1, X2, (d) It can be derived that and n. Use the notation: Xn) fx) (x) = 1 21 x-(-n) 2n n-1 x = [-nu+n] fx(m) (x) x- (-n) n-1 21 21 Determine whether the estimate obtained by the Method of Maximum Likelihood is biased for . Hint: Use substitutions y = 1- 1-(1-1) and y') 2 21 (e) Describe the criteria which can be used to choose between these two estimates. Suppose we have X1, X2, X, which are i.i.d. and come from the uniform distribution Uniform(+) > 0; 0 = (m) (a) Use the Method of Moments to estimate and 1. (b) Determine whether the estimate derived by the Method of Moments is biased for . (c) Use the Maximum Likelihood method to estimate X(1) = min(X1, X2,..., Xn) and X(n) = max(X1, X2, (d) It can be derived that and n. Use the notation: Xn) fx) (x) = 1 21 x-(-n) 2n n-1 x = [-nu+n] fx(m) (x) x- (-n) n-1 21 21 Determine whether the estimate obtained by the Method of Maximum Likelihood is biased for . Hint: Use substitutions y = 1- 1-(1-1) and y') 2 21 (e) Describe the criteria which can be used to choose between these two estimates.