B1. Suppose we have X₁, X2, ... Xn, which are i.i.d. and come from the uniform distribution Uniform(μ-n, μ+n), n>0;0= (μ, n) (a) Use the Method of Moments to estimate μl and n. (b) Determine whether the estimate derived by the Method of Moments is biased for μ. (c) Use the Maximum Likelihood method to estimate and n. Use the notation: X(1) = min (X₁, X2,..., Xn) and X(n) = max(X₁, X2,..., Xn) (d) It can be derived that fx₁)(x) = n 2/17 (1- 2η x = [μ = n₂ μ+ n], E χε[μ - ημ + η] Determine whether the estimate obtained by the Method of Maximum Likelihood is biased for . Hint: Use substitutions y = 1 fx(n)(x) = = X- n 2η X- n-1 27 ・(μ-n)` 2n n-1 x-(μ-n) and y' 2n 2 x-(μ-n) 2n (e) Describe the criteria which can be used to choose between these two estimates. =

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