I have a random variable $\gamma$, which is product of two normal random variable $h_{st},h_{tr}$ and they are related as $\gamma = \eta\cdot h_{st}\cdot h_{tr}$. The PDF of $\gamma$ is given as
$f_{\gamma}(x) = \frac{1}{\pi\eta\sqrt{\sigma_{st}^2\sigma_{tr}^2}}K_0\left(\frac{|x|}{\eta\sqrt{\sigma_{st}^2\sigma_{tr}^2}}\right)$ -----(1)
From the Simon book "Probability distributions involving Gaussian Random Variables: a handbook for engineers and scientists.", i know that the PDF of product of two Gaussian random variables is the same eq.(1) except the presence of $\eta$ factor. I am having doubt about how the $\eta$ factor is coming in eq. (1). Any help in this regard is highly appreciated...