1. Given current technology, the production of active matrix color screens for notebook computers is a difficult process that results in a significant proportion of defective screens being produced. At one company the daily proportion of defective 9.5" and 10.4"

screens is the outcome of a bivariate random variable, X, with joint density function f(xl, X2;

a) := (axl + (2 -

a)x2)Ijo,lj(xl JIjO.lI(X2J, where a E (0,2). The daily proportions of defectives are independent from day to day. A collection of n iid outcomes of X will be used to generate an estimate of the (2 xl) vector of mean daily proportions of defectives, f.L, for the two types of screens being produced, as Xn := 2:::1 X;/n, where Xj := [;Ii).

12xl) 2,

-as -p -d

a. Does Xn -4 pl Does Xn -4 pl Does Xn ---t pl