About parameter of exponentially distributed random variable

Question

In the attached figure, $h_{sr},h_{re_i},h_{ru_i}\sim \exp(1)$. How can authors claim that SNR is exponentially distributed with the rate as mentioned? Note that $\Gamma_r,\Gamma_{u_i}, \Gamma_{e_i}$ are SNRs (with noise normalized to 1)

Answer 1

Actually it is a very simple property of exponential distribution i.e. if $X\sim \exp(\lambda)$ with parameter $1/\lambda$, then $cX\sim \exp(\lambda/c)$ with parameter $c/\lambda$.

See for example: https://en.wikipedia.org/wiki/Exponential_distribution#Related_distributions