(164) 5. In the textbook Exercise 5.10, we had to show that f()1, y2) = 1, 0 5 y, $ 2, 0 5 y2 5 1, 2y2 3 yIs 0, elsewhere is a valid joint probability density function for Y1, the amount of pollutant per sample collected above the stack without the cleaning device, and Y2, the amount collected above the stack with the cleaner. (a) (4 pts) Find E(Y,) and E(Y2). (b) (4 pts) Find V(Y ) and V(Y2). (c) (4 pts) The random variable Y, - Y2 represents the amount by which the weight of pollutant can be reduced by using the cleaning device. Find E(Y, - Y2). (d) (4 pts) Find V(Y, - Y2). (Hint: You will need to use the fact that V(Y - YZ) = E(, - Y)1-LECK- Y2)12 to solve this.) Bonus: Within what limits would you expect Y1 - Yz to fall