Gasoline is to be stocked in a bulk tank once at the beginning of

each week and then sold the individual customers. Let X denote the

proportion of the capacity of the bulk tank that is stocked at the

start of the week. Let Y denote the proportion of the capacity of

the bulk tank that is sold during the week. Because X and Y are both

proportions, both variables take on values between 0 and 1. Further,

the amount sold, Y, cannot exceed the amount available, X. Suppose

that a joint pdf model for X and Y is given by:

f(x,y) = 3x for 0 <= y <= x <= 1, 0 for elsewhere

Find the pdf for U = X - Y, the proportional amount of gasoline

remaining at the end of the week. Use the pdf of U to find the

expected value of U, E(U). Use the pdf of U to find the probability

that the proportional amount of gasoline remaining at the end of

the week, U, is between 0.25 and 0.5.

If anyone can help me get the problem started or guide me in the right direction, it would be greatly appreciated. I'm not sure how to start this problem.