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In the context of communication systems, Rayleigh random variables arise as the amplitude of received signals. A model for such a signal is $$X\cos(\omega_0 t)- Y \sin(\omega_0 t) = R \cos(\omega t + \Theta)\tag{1}$$ where $X$ and $Y$ are independent Gaussian random variables with the same variance $\sigma^2$, which can be expressed as the right side of $(1)$ with $R$ being a Rayleigh random variable and $\Theta$ uniformly distributed on $[0,2\pi)$; $R$ and $\Theta$ are independent too. The intuitive explanation for the model is that a transmitted signal $A\cos(\omega t)$ is reflected off many scatterers resulting in a received signal that is formed by the sum of many tiny (small-amplitude) reflections. The Central Limit Theorem then allows us to pretend that the resulting sum as a Gaussian random variable. The right side of $(1)$ should also be familiar to statisticians as the linchpin of the linchpin of the Box-Muller method for generating samples of Gaussian random variables.