Although this question has been extensively studied since 100 years ago, I am getting tired of not finding an answer for this in the literature:
If $X_i$s are independent normal random variables with mean $\mu_i$ and variance $\sigma_i^2$, then what is the probability density function (PDF) of $z=\sum_{i=1}^{n}X_i^2$?
Can you please give me a closed form of the PDF and the CDF?