41. A stick is 1 foot long. You break it at a point X (measured from the left end) chosen randomly uniformly V1Y X  x2 E1Y X  x2 E1Y X  x2 E1X Y  y2 along its length. Then you break the left part at a point Y chosen randomly uniformly along its length.

In other words, X is uniformly distributed between 0 and 1 and, given X  x, Y is uniformly distributed between 0 and x.

a. Determine and then . Is x) a linear function of x?

b. Find f (x, y) using fX(x) and

c. Find fY(y).