Let $X_1, X_2$ be i.i.d. $\sim \mathcal{N}(0, 1)$.
How can I find $P(X_1^4+X_2^4 < 3)$?
There is a similar question, but instead of the sum of squares of $\chi^2_1$ the question is about the square of their sum.
It seems like a possible solution is to take the integral of joint density function of two normal random variables with those borders, but I'm wondering if a more elegant solution exists.
