If $Y = \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 the resultant PDF of $Y$ can be interms of Gamma distribution?
I know that, if the mean is zero, the result follows as given in Relationship between gamma and chi-squared distribution, but how it can be derived for the case if the mean is zero?