What it the distribution for square root of sum of squares of two independent normal distributed random variable? Assuming they have zero mean and same non-zero variance. Suppose $X$ and $Y$ ~ $N(0,\sigma^2)$, what is the distribution for $Z = \sqrt{X^2+Y^2}$? Looking for any feedbacks or comments.

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    $\begingroup$ Hint: $X^2+Y^$ is an exponential random variable. $\endgroup$ May 16, 2017 at 23:15
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    $\begingroup$ See en.wikipedia.org/wiki/Chi_distribution. $\endgroup$
    – whuber
    May 16, 2017 at 23:39
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    $\begingroup$ This reads like a textbook-style exercise (it's certainly simple enough to be one). In any case "looking for any feedback" is a bit too general (you didn't do anything to give feedback on). Can you be more explicit about the source of the problem? $\endgroup$
    – Glen_b
    May 16, 2017 at 23:56
  • $\begingroup$ This is related to the Raleigh distribution. That is $Z/\sigma$ has Raleigh distribution. I assume that you are taking the positive square root as is conventional. $\endgroup$ May 17, 2017 at 0:40
  • $\begingroup$ Is there also a "named" distribution, if the expectation values of X and Y are non zero? $\endgroup$
    – MiB_Coder
    Feb 2, 2021 at 20:11