# Let , be independent N(0,1) distributed random variables. Define and . Without using calculus, show that...

Let $X_1$, $X_2$ be independent N(0,1) distributed random variables. Define $W_1 = X_1^2 + X_2^2$ and $W_2 = \frac{X_1^2 - X_2^2}{X_1^2 + X_2^2}$ . Without using calculus, show that $W_1 \perp W_2$.

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W1 = x + x
x1 - x x} + Xž
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