# How to find this probability with PDF from TransformedDistribution?

I need to find the expression for the following equation, where $m>0$

Probability[y≤m,y\[Distributed]TransformedDistribution[x^2,x\[Distributed]RiceDistribution[v,Sqrt[α/2]]]]


But, MMA does not give me what I want. any help. Am I using the right syntax?

• 1) I has a special meaning in Mathematica as the imaginary unit, so you shouldn't use it as your variable; more in general, try to avoid uppercase variable names altogether. 2) when you specify the distribution of y, I think you should use the transformed distribution directly, not its PDF. – MarcoB Apr 26 '16 at 12:32
• – MarcoB Apr 26 '16 at 12:52
• @MarcoB, thanks for your comment. I have tried with your suggestion. It still does not work...... – Srestha Narayanan Apr 26 '16 at 12:53
• Have you tried writing the integral yet? Are you familiar without how to do that? Use PDF to get the PDF of the Rice Distribution. Integrate[( 2 E^(-((t^2 + v^2)/[Alpha])) t BesselI[0, (2 t v)/[Alpha]])/[Alpha] t^2, {t, 0, m}] – Searke Apr 26 '16 at 13:27
• There's no reason to believe there's a solution to this problem. You may have to use an approximation instead. – Searke Apr 26 '16 at 13:42

PDF[TransformedDistribution[x^2, x \[Distributed] RiceDistribution[v, Sqrt[α/2]]], y]

Just change PDF to CDF (and avoid the use of I as @MarcoB recommended):
CDF[TransformedDistribution[x^2, x \[Distributed] RiceDistribution[v, Sqrt[α/2]]], y]