We know that if
x \[Distributed] ExponentialDistribution[λ]
then
y = Sqrt[x] \[Distributed] RayleighDistribution[1/Sqrt[2*λ]]
Which we can justify by the following:
Dist = RayleighDistribution[1/Sqrt[2*λ]];
SDist = TransformedDistribution[x^2, x \[Distributed] Dist]
On the other hand, we also know that if
r \[Distributed] RiceDistribution[0, σ]
then
r \[Distributed] RayleighDistribution[σ]
But by the following code, I do not get an Exponential Distribution. Why?
Dist = RiceDistribution[0, 1/Sqrt[2*λ]];
SDist = TransformedDistribution[x^2, x \[Distributed] Dist]