'''Rayleigh Random Variable'''

$S_X=[0,\infty)$

$f_X(x)=\frac{x}{\alpha^2}e^{-x^2/2\alpha^2}$
 $x\ge0,\,\alpha\gt 0$

$E[X]=\sqrt{\frac{\pi}{2}}\alpha$

$V[X]=\left(2-\frac{\pi}{2}\right)\alpha^2$

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Source: Leon-Garcia Table 4.1 (Continuous RVs)
Up: [[연속확률변수,continuous_RV]]