The random vector X = (X, X)' is bivariate normally distributed with = (0, 0)' and...

 

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The random vector X = (X, X)' is bivariate normally distributed with = (0, 0)' and covariance matrix Ex = (). expectation x a. Prove that Y = X pX and Y = X are independent without (explicitly) using probability densities. b. Notice that X = (X, X)' and Y = (Y, Y)' are linearly related, i.e. Y = A. X, with A a 2 x 2 matrix. Use the formulae y = A x and Ey = A. Ex A' to obtain the expectation y and covariance matrix Zy of Y. . The random vector X = (X, X)' is bivariate normally distributed with = (0, 0)' and covariance matrix Ex = (). expectation x a. Prove that Y = X pX and Y = X are independent without (explicitly) using probability densities. b. Notice that X = (X, X)' and Y = (Y, Y)' are linearly related, i.e. Y = A. X, with A a 2 x 2 matrix. Use the formulae y = A x and Ey = A. Ex A' to obtain the expectation y and covariance matrix Zy of Y. .