When I try to exploit this Rayleigh distribution *Mathematica* couldn't answer. PDF[TransformedDistribution[ Sqrt[x1^2 + x2^2], {x1 \[Distributed] NormalDistribution[μ1, σ], x2 \[Distributed] NormalDistribution[μ2, σ]}, Assumptions -> μ1 == μ2 == 0], r]