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

Airplane speeds are measured in three different ways: (1) indicated speed, (2) true speed, and (3) ground speed. the indicated airspeed is the airspeed given by an instrument called an airspeed indicator. a plane’s indicated airspeed is different from its true airspeed because the indicator is affected by temperature changes and different altitudes of air pressure. the true airspeed is the speed of the airplane relative to the wind. ground speed is the speed of the airplane relative to the ground. for example, a plane flying at a true airspeed of 150 knots into a headwind of 25 knots will have a ground speed of 125 knots. the problems below refer to static and dynamic pressure. static pressure is used when a body is in motion or at rest at a constant speed and direction. dynamic pressure is used when a body in motion changes speed or direction or both. a gauge compares these pressures, giving pilots an indicated airspeed. in problem #s 1 and 2, use the following information. the indicated airspeed s (in knots) of an airplane is given by an airspeed indicator that measures the difference p (in inches of mercury) between the static and dynamic pressures. the relationship between s and p can be modeled by s=136.4p√+4.5. 1. find the differential pressure when the indicated airspeed is 157 knots. 2. find the change in the differential pressure of an airplane that was traveling at 218 knots and slowed down to195 knots. in problem #s 3 and 4, use the following information. the true airspeed t (in knots) of an airplane can be modeled by t=(1+a50,000) ⋅ s, where a is the altitude (in feet) and s is the indicated airspeed (in knots). 3. write the equation for true airspeed t in terms of altitude and differential pressure p. 4. a plane is flying with a true airspeed of 280 knots at an altitude of 20,000 feet. estimate the differential pressure. explain why you think your estimate is correct.

Candy lives in the center of town. her friend darlene lives 28 miles to the east and her friend dana lives 21 miles north. approximately how far do dana and darline live apart ?

Need ! the total ticket sales for a high school basketball game were $2,260. the ticket price for students were $2.25 less than the adult ticket price. the number of adult tickets sold was 230, and the number of student tickets sold was 180. what was the price of an adult ticket?