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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 W1 = x + x and x1 - x x} + Xž . 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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without using calcutus, So we cant use P [ W, W2] = p (Wil. PlWe] I which is the actual method to prove independence. so onlthen x + x and X - X are independent. - x²+x2 and x2 x ² are independent - (Bince linearity property of normal distsibution)

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