4.2 Let X : p × 1 denote the scores of unemployed males 18-60 years of age, in a ghetto area, on a battery of p tests of their job skills and abilities. Let Xj, j = 1, ... ,N denote the vector of scores for the jth subject, and , the scores for the sample mean vector for N independent observations. Let E(Xj) = θ, and var (Xj) = Σ, j = 1, ..., N. Let f( ) denote a scalar function which is used as a general measure of the job skill level of the group taking the battery of tests. Suppose where b is a known scalar, a is a known p × 1 vector, and is a p × 1 vector whose ith component is log ( ) (see Exercise 2.8). Find the asymptotic distribution of f( ) so that inferences can be drawn about the population from which the group was drawn.