A point [math]Y[/math] is chosen at random from [math][0,1][/math]. A second point [math]X[/math] is then chosen from the interval [math][0,Y][/math]. Find the density for [math]X[/math]. Hint: Calculate [math]f_{X|Y}[/math] as in Exercise Exercise and then use

[[math]] f_X(x) = \int_x^1 f_{X|Y}(x|y) f_Y(y)\, dy\ . [[/math]]

Can you also derive your result geometrically?