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How do I find the probability density distribution (pdf) of the difference of independent Rayleigh random variables (whose probability density functions are known)? Assume $X$, $Y \sim \text{Rayleigh}(\sigma)$, $X$ and $Y$ are i.i.d. Then what distribution is $X-Y$? Can anyone derive it from Maple or Mathematica? Or even better, through integral (I tried it but failed).

Thanks in advance!

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