I have $X_1 \sim N(0, 4), X_2 \sim N(0, 4), X_3 \sim N(3, 1), X_4 \sim N(1, 9)$, they are independent. I need to find cumulative distribution function of $\xi = \frac{X_3X_2 + X_4X_1}{ \sqrt{X_4^2 + X_3^2}} $. Can you give me any clues? Thanks.
2025-01-12 23:31:48.1736724708
Cumulative distribution function of function of normal random variables
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