I have independent random variables $X_1$, $X_2$ such that $X_1 \sim N(1,1)$ and $X_2 \sim N(2,2)$, and I'm trying to find a constant $a$ such that $a(X_1 - X_2 + 1)^2$ has a chi-squared distribution.
I'm pretty sure that the sum of $y=(X_i + X_j)^2$ generally is a chi-squared distribution. But the process is eluding me, so could use some help.