Consider a column-vector w containing two random variables denoted X and Y. That is w = [X Y]T. Assume the following: (i

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Consider A Column Vector W Containing Two Random Variables Denoted X And Y That Is W X Y T Assume The Following I 1 (120.29 KiB) Viewed 63 times

Consider a column-vector w containing two random variables denoted X and Y. That is w = [X Y]T. Assume the following: (i) E[X] = 0, E[Y] = 0, (ii) E[X²] = 02, E[Y2] = 0;, (iii) E[XY] = Oxy #0 (a) Derive the variance-covariance matrix of w. (b) Calculate the determinant of the variance-covariance matrix you derived in (a). Would the variance-covariance matrix be invertible if X and Y were perfectly correlated. Justify your answer. (c) Let d [d11 012] be a row-vector containing non-random elements. Calculate the variance of dw.