* hr ry ° aq ™ * ime i > (3) this set of MSS is complete, and (4) any function of the MSS is an MVUE if the function is unbiased. E(X) To see that x is unbiased, E(X, + X, 2 +...+ X)/n [E(x,) + E(x.) +...+ E(x) ]/n (n u)/n Hence X is an MVUE of EX. Mood et al. (1974). The details of this proof can be obtained in The result that x is an MVUE is particularly fortu- itous as the arithmetic mean of the sample has often been used to estimate EX for real data. The usual confidence intervals for x, namely x t t(n-1) s/vn ; will be used, with the Central Limit Theorem and the asymptotic normality of an MLE to justify the assumption of normality. Because of this assumption, this confidence interval may perform poorly for small sample sizes. The variance estimate thus obtained is not the same as the variance of x calculated by the maximum likelihood estimation procedure. However, the calculations are much easier to perform, and this estimator is the one commonly used in the transuranic literature. Therefore, of interest is whether confidence intervals based on this simple variance estimator are valid. Of particular concern is the validity of this approach for small sample sizes, say n = 5. ROBUSTNESS Both estimators described above are known to have optimal properties when used with data derived from their respective distributions. In addition, the performance of each estimator when applied to other distribution functions is of interest, i.e., how robust the estimator may be. 613