Plain english explanation of the Rayleigh distribution? I need to understand the Rayleigh distribution for a homework assignment in computer networks. Unfortunately, I lack the background knowledge in the field of statistics and probability theory to understand the descriptions that are given elsewhere about the Rayleigh Distribution, as it leads me from one page to another and I get more confused.
If you could use an example to illustrate the case it would be even more useful. 
 A: In the context of communication systems, Rayleigh random variables arise as the amplitude of received signals. A model for such a signal is
$$X\cos(\omega_0 t)- Y \sin(\omega_0 t) = R  \cos(\omega_0 t + \Theta)\tag{1}$$
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 $A\cos(\omega_0 t)$ 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 Box-Muller method for generating samples of Gaussian
random variables.
If your work in computer networks deals with reliability of systems
and networks, then you should know that if a hazard rate is assumed
to be increasing linearly with time, then the lifetime of the system
is a Rayleigh random variable.
