The Basic Model Consider again the basic statistical model, in which we have a random experiment that results in an observable random variable X taking values in a set S . Once again, the experiment is typically to sample n objects from a population and record a vector of measurements for each item. Note that the expected value , variance , and covariance operators also depend on a , although we will suppress this to keep the notation from becoming to unwieldy. Finally, let D a denote the derivative operator with respect to a . Then U is a uniformly better estimator than V .
V has smaller variance for other values of a .
Show that this condition is equivalent to the assumption that the derivative operator D a can be interchanged with the expected value operator E . Now let h be a function that satisfies the basic condition. Then simply use the basic condition. The variable has mean 0. 5. The joint density is the product of the marginal densities.