Casualty Actuarial Society MAS-1 Practice Exam 2026 – Your All-in-One Guide to Mastering the Exam!

The MVUE is found by using a complete sufficient statistic for the parameter and an unbiased estimator. For an inverse Gaussian distribution with the mean parameter mu and a known shape parameter lambda, the sum of the observations is a complete sufficient statistic for mu. The mean of each X_i is mu, so the sample mean X_bar is unbiased for mu. Since X_bar is just the sum divided by n, it is a function of the complete sufficient statistic. By the Rao-Blackwell principle, an unbiased estimator that is already a function of the complete sufficient statistic is the best unbiased estimator, i.e., the MVUE. Therefore, the MVUE of the mean parameter is the sample mean X_bar. (If lambda were also unknown, the complete sufficient statistic would involve both sum Xi and sum 1/Xi, and the reasoning would differ.)