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

Jobs and productivity! how do retail stores rate? one way to answer this question is to examine annual profits per employee. the following data give annual profits per employee (in units of 1 thousand dollars per employee) for companies in retail sales. assume σ ≈ 4.0 thousand dollars. 3.7 6.7 3.6 8.5 7.5 5.9 8.7 6.4 2.6 2.9 8.1 −1.9 11.9 8.2 6.4 4.7 5.5 4.8 3.0 4.3 −6.0 1.5 2.9 4.8 −1.7 9.4 5.5 5.8 4.7 6.2 15.0 4.1 3.7 5.1 4.2 (a) use a calculator or appropriate computer software to find x for the preceding data. (round your answer to two decimal places.) thousand dollars per employee (b) let us say that the preceding data are representative of the entire sector of retail sales companies. find an 80% confidence interval for μ, the average annual profit per employee for retail sales. (round your answers to two decimal places.) lower limit -- thousand dollars upper limit -- thousand dollars (c) let us say that you are the manager of a retail store with a large number of employees. suppose the annual profits are less than 3 thousand dollars per employee. do you think this might be low compared with other retail stores? explain by referring to the confidence interval you computed in part (b). yes. this confidence interval suggests that the profits per employee are less than those of other retail stores. no. this confidence interval suggests that the profits per employee do not differ from those of other retail stores. correct: your answer is correct. (d) suppose the annual profits are more than 6.5 thousand dollars per employee. as store manager, would you feel somewhat better? explain by referring to the confidence interval you computed in part (b). yes. this confidence interval suggests that the profits per employee are greater than those of other retail stores. no. this confidence interval suggests that the profits per employee do not differ from those of other retail stores. (e) find an 95% confidence interval for μ, the average annual profit per employee for retail sales. (round your answers to two decimal places.) lower limit 3.75 incorrect: your answer is incorrect. thousand dollars upper limit 6.41 incorrect: your answer is incorrect. thousand dollars