123. A circular target has radius 1 foot. Assume that you hit the target (we shall ignore misses) and that the probability of hitting any region of the target is proportional to the region’s area. If you hit the target at a distance Y from the center, then let X 

pY2 be the corresponding circular area. Show that

a. X is uniformly distributed on [0, p]. Hint:

Show that FX(x)  P(X x)  x/p.

b. Y has pdf fY(y)  2y, 0  y  1.