Suppose that x -wage income, and u -nonwage income, and suppose that (x, u) are bivariate normal with e(x) = 30, e(u) = 5, var(x) = 185, var(u) = 35, and cov(x, u) = 15. suppose total income is y = x + u all variables are measured in thousands of dollars.
(a) what is e(y|x = x)?
(b) what is var(y|x=x)?
(c) what is e(x|y=y?
(d) what is var(x|y=y)?
(e) what is the distribution of y given x?
(f) what is the distribution of x given y?
(g) a person reports her wage income to be x-20. calculate the probabil- ity that her total income is less than 20. you may express your result ir terms of φ
(h) a person reports her total income to be y -20. calculate the probability hat her wage income is less than 20. you may express your result in terms of φ