Let $X_1, X_2, \ldots X_n$ be independent Gaussian random variables with $N(0,1)$ distribution. Find the density and the characteristic function of $X_1^2 + X_2^2 + \cdots + X_n^2$
I am preparing for exams and I am stuck with this particular problem. I have seen the derivation for the characteristic function of a standard normal random variable. But I tried calculating the integral for the square and I cannot get it. Once I do that though, I think I can just raise my answer to the nth power to account for the sum. Can someone please help me with this? I have been stuck and not sure for many hours.