Lett U1, U2, U3 i.i.d. uniform(0,1) and let Y1 < Y2 < Y3 represent their order statistics. Use the method of Jacobians to derive the pdf of Y3 Y1, the so-called sample range in statistics. Hint: You can start by first setting up a one-to-one transformation U = Y3 Y1 and V = Y3, say.

9.4. (continued from 9.3.) Find the pdf of the median Y2 in any way you choose