Problem IV. (30 points). Be sure to show all work for full credit. A fast food restaurant operates both a drive-in-through facility and a walk-in facility. On a randomly selected day, let X and Y, respectively, be the proportions of time that the drive-through and walk-in facilities are in use, and suppose that the joint density function of these random variables is ( 6(x+y)?,0 SX S1,0 sys1 f(x,y) = { 0 elsewhere

Problem IV. (30 points). Be sure to show all work for full credit. A fast food restaurant operates both a drive-in-through facility and a walk-in facility. On a randomly selected day, let X and Y, respectively, be the proportions of time that the drive-through and walk-in facilities are in use, and suppose that the joint density function of these random variables is 6(xty)2 7 0