Suppose that Y1 and Y2 follow a bivariate normal
Chapter , Problem 57(choose chapter or problem)
Suppose that \(Y_1\) and \(Y_2\) follow a bivariate normal distribution with parameters \(\mu_{Y_{1}}=\mu_{Y_{2}}=0, \sigma_{Y_{1}}^{2}=1, \sigma_{Y_{2}}^{2}=2\) and \(\rho=1 / \sqrt 2\). Find a linear transformation \(x_{1}=a_{11} y_{1}+a_{12} y_{2}, x_{2}=a_{21} y_{1}+a_{22} y_{2}\) such that \(x_1\) and \(x_2\) are independent standard normal random variables. (Hint:See Example C of Section 3.6.2.)
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