I wonder how to implement below derivation in wolfram mathematica. I want to see integrate results like below picture. Can you help. I used "TransformedDistribution" but it shows only distribution name.

Picture from : Athanasios Papoulis - Unnikrishna Pillai - Probability, Random Variables and Stochastic Processes -McGraw-Hill Europe (2002) page 190.


  • $\begingroup$ Mathematica is not designed to give step-by-step solutions. In general, the algorithms that it uses are not the ones that you might use when doing a problem. For simpler problems, the WolframAlpha command may offer a step-by-step solution. f[z_] = PDF[TransformedDistribution[x^2 + y^2, {x \[Distributed] NormalDistribution[0, σ], y \[Distributed] NormalDistribution[0, σ]}], z] $\endgroup$ – Bob Hanlon Oct 15 at 13:33
  • $\begingroup$ If you need the steps to the integration, then you might consider Rubi (rulebasedintegration.org). There's also a missing "-" in the first equation: $(z-y^2+y^2)/2\sigma^2$ should be $-(z-y^2+y^2)/2\sigma^2$. $\endgroup$ – JimB Oct 15 at 15:28

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