If $Y = \sqrt{\sum_{i=1}^N X_i^2} $, where $X_i \sim \mathcal{N}(\mu,\sigma^2)$, i.e. all $X_i$ are i.i.d gaussian random variables of same mean and variance, then what is the resultant PDF of $Y$? How to calculate the mean and variance of the resultant pdf?

  • 2
    $\begingroup$ This is only a slight variation of your other answered question - since you already know you need to look at the noncentral chi distribution, it is worth looking up this distribution first. Does this clarify your question? $\endgroup$
    – Ben
    Jul 2, 2018 at 10:38
  • 1
    $\begingroup$ It should be possible to adapt the technique from: stats.stackexchange.com/questions/317095/… $\endgroup$ Jul 2, 2018 at 10:56
  • $\begingroup$ @Ben No sir, no clarity $\endgroup$ Jul 2, 2018 at 12:55
  • $\begingroup$ With the information @Ben gave you, you can now look up the answer. Is that what you seek, or do you want to know how the solution is derived? $\endgroup$
    – whuber
    Jul 2, 2018 at 13:43


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.