(25 points) Let X = (X,..,X) be a random sample from the distribution of a RV...

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(25 points) Let X = (X,..,X) be a random sample from the distribution of a RV X with pdf: f(x, 0) = e(x0) I (0.2)(x), OER. (a) Find a minimal sufficient statistic T(X) for 0. (b) Show that the statistic T(X) obtained in part (a) is a complete sufficient statistic for O. (c) Let S be the sample variance. Show that the statistic T(X) obtained in part (a) and S are independent. (d) Find the UMVUE for 0. (25 points) Let X = (X,..,X) be a random sample from the distribution of a RV X with pdf: f(x, 0) = e(x0) I (0.2)(x), OER. (a) Find a minimal sufficient statistic T(X) for 0. (b) Show that the statistic T(X) obtained in part (a) is a complete sufficient statistic for O. (c) Let S be the sample variance. Show that the statistic T(X) obtained in part (a) and S are independent. (d) Find the UMVUE for 0.