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This question already has an answer here:

Let $X$ and $Y$ be two independent random variables. If $X$ and $Y$ are both standard normal, then what is the distribution of the random variable $$\frac{1}{2}(X^2+Y^2)$$

Is it right that the answer to this question is $$\frac{1}{2}(X^2+Y^2) \texttt{ ~ } EXP(1)$$? But how? Thank you very much, any help will be much appreciated.

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marked as duplicate by Did, Davide Giraudo, Namaste, Aweygan, NCh May 8 '17 at 18:39

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

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    $\begingroup$ You can find the answer here, here, here or here $\endgroup$ – caverac May 8 '17 at 10:22
  • $\begingroup$ How did it arrive to an EXP distribution? $\endgroup$ – geniwebb May 8 '17 at 11:02
  • $\begingroup$ Much appreciated. Thanks! $\endgroup$ – geniwebb May 8 '17 at 12:32
  • $\begingroup$ I add here the reference: Charles M. Grinstead and J. Laurie Snell, Introduction to Probability, American Mathematical Society (2003). $\endgroup$ – user243301 May 8 '17 at 12:45