The random variables (xi) and (eta) are independent and are normally distributed with the same parameters (a)
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The random variables \(\xi\) and \(\eta\) are independent and are normally distributed with the same parameters \(a\) and \(\sigma\). Find the correlation coefficient of the quantities \(\alpha \xi+\beta \eta\) and \(\alpha \xi-\beta \eta\), and also their joint distribution.
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