Let $X_1$, $X_2$, $X_3$, $X_4$ have the joint pdf $f(X_1,X_2,X_3,X_4) = 24$ , $0 < X_l < X_2 < X_3 < X_4 < 1$ , $0$ elsewhere. Find the joint pdf of $Y_1 = X_1/X_2$, $Y_2 = X_2/X_3$ , $Y_3 = X_3/X_4$, $Y_4 = X_4$ and show that they are mutually independent.
I know they joint pdf is $24y_2(y_3^2)(y_4^2)$ but how do I show they are mutually independent?