1.4 (

) www Consider a probability density px(x) defined over a continuous variable x, and suppose that we make a nonlinear change of variable using x = g(y), so that the density transforms according to (1.27). By differentiating (1.27), show that the location
y of the maximum of the density in y is not in general related to the location
x of the maximum of the density over x by the simple functional relation

x = g(
y) as a consequence of the Jacobian factor. This shows that the maximum of a probability density (in contrast to a simple function) is dependent on the choice of variable. Verify that, in the case of a linear transformation, the location of the maximum transforms in the same way as the variable itself.