Let X = (X, X2,..., X,) be a sample from the U (a, B) distribution. It is desired to estimate the mean 0 = (a+B)/2

Let X = (X₁, X2,..., X,) be a sample from the U

(a, B) distribution. It is desired to estimate the mean 0 = (a+B)/2 under squared-error loss.

(a) Show that T=(min{X,}, max{X}) is a sufficient statistic for 0. (You may use the factorization theorem.)

(b) Show that the estimator given by E*T[X]=}(max{X,} +min{X,})

is R-better than or R-equivalent to the sample mean X.