G Suppose (X, Y ) is a bivariate normal random variable, BVN(0, 0, 1, 1, rho), where X, Y are standard normal random variables and corr(X, Y ) = rho. Show that Y − rhoX and X are independent random variables.

Data from 2005 for various age groups show that for each $100 increase in the median weekly income for whites, the median weekly income of blacks increases by $105. also, for workers of ages 25 to 54 the median weekly income for whites was $676 and for blacks was $527. (a) let w represent the median weekly income for whites and b the median weekly income for blacks, and write the equation of the line that gives b as a linear function of w. b = (b) when the median weekly income for whites is $760, what does the equation in (a) predict for the median weekly income for blacks?