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) = 100, var(u) = 40, and cov(x, u) = 2. suppose total income is y = x + u. all variables are measured in thousands of dollars. you do not need a calculator for this problem, you do not need to simplify algebraic statements. a. what is the distribution of y given x? b. what is the distribution of x given y? c. a person reports her wage income to be x=20. calculate the probability that her total income is less than 20. you may express your result in terms of φ.d. a person reports total income to be y = 20. calculate the probability that her wage income is less than 20. you may express your result in terms of φ.