Consider randomly selecting a point (x1, x2, x3) in the unit cube {(x1, x2, x3): 0 < x1 < 1, 0 < x2 < 1, 0 < x3 < 1}according to the joint pdf fðx1; x2; x3þ ¼ 8x1x2x3 0 < x1 < 1; 0 < x2 < 1; 0 < x3 < 1 0 otherwise ( (so the three variables are independent). then form a rectangular solid whose vertices are (0, 0, 0), (x1, 0, 0), (0, x2, 0), (x1, x2, 0), (0, 0, x3), (x1, 0, x3), (0, x2, x3), and (x1, x2, x3). the volume of this cube is y3 ¼ x1x2x3. obtain the pdf of this volume. [hint: let y1 ¼ x1 and y2 ¼ x1x2.]