I had confusion in understanding whether the two PDFs are same? Let $h$ is normally distributed with mean $0$ and variance $\sigma^2$. Now another random variable $\rho$ is defined as $\rho=h^2\cdot\rho_t$. Therefor PDF of $\rho$ i.e.,
$$\tag{1} f_{\rho}(x) = \frac{f_{|h|^2}(x/\rho_t)}{x\rho_t}$$
. Similarly,
$$\tag{2}f_{\rho}(x) = \frac{f_{|h|}(\sqrt{x/\rho_t})}{\sqrt{x\rho_t}}$$
Are the PDF in equation (1) and (2) same? Any help please, Thank you .