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.

In may you used 400 kilowatt-hours of energy for electricity. a. calculate the total electrical energy use in joules. b. calculate your average power use in watts. c. assume that your power supplier generates electricity by burning oil. note that 1 liter of oil releases 12 million joules of energy. how much oil is needed to generate the electricity you use? give your answer in both liters and gallons. a. the total electrical energy use was nothing _ joules. (type an integer or a decimal.) b. the average power use is nothing _ watts. (round to the nearest whole number as needed.) c. to generate the electricity you used, nothing _ l is needed. (round to the nearest whole number as needed.) to generate the electricity you used, nothing _ gal is needed. (round to two decimal places as needed.)