# How to calculate mean and variance of non central chi distribution of the problem?

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?

• 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?
– Ben
Jul 2, 2018 at 10:38
• It should be possible to adapt the technique from: stats.stackexchange.com/questions/317095/… Jul 2, 2018 at 10:56
• @Ben No sir, no clarity Jul 2, 2018 at 12:55
• 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?
– whuber
Jul 2, 2018 at 13:43