Can someone clear my doubt related to difference between random variable and simple variable. My question is as follows:
Say, I have three wireless channels that are random in nature and are denoted as $h,g,f$. These channels are distributed as $x\sim \mathcal{C}{N}(0,\sigma^2_{x})$, $x\in[h,g,f]$ and $\sigma^2_{x} = 2$. And from their combination, another random channel is formed denoted by $\beta$, where $\beta$ is,
$\beta = h+\alpha gf$
where $\alpha $ is constant with value $0.5$.
Next, it is assumed in one of the research paper that $g$ will be constant (due to very less distance between two nodes). Thus as per my understanding, now $\beta$ will also be distributed as $\beta\sim \mathcal{C}{N}(0,\sigma^2_{\beta})$ and the variance of $\beta$ will be
$\sigma^2_{\beta} = \sigma^2_{h}+\alpha^2 g^2 \sigma^2_{f}$....(1)
Now my doubt is what should we substitute in (1) in place of $g^2$ as other values such as $\alpha^2, \sigma^2_h, \sigma^2_f$ are available.
Any help in this regard will be highly appreciated.