Question: 3 1 1 3 4 X Suppose X~ ~N. (2), where = 1 5 5 8 and 22 3 5 11 11 44 4

3 1 1 3 4 X Suppose X~ ~N. (2), where = 1 5 5 8 and 22 3 5 11 11 44 4 8 11 33 (a) Determine the following: (i) The marginal distribution of X4 [2 marks] (x (ii) The marginal distribution of (X2) [9 marks] (iii) The conditional distribution of X1 and X2, given X3 = -2 and X4 = 3. [22 marks] (iv) The marginal distribution of Y = 3X-X+2X4 [10 marks] (v) The joint distribution of Y = 3X - X+X4 -X+4X+2X/ [9 marks] (vi) Cov(X2, X + X) [3 marks] (vii) Cov(2X, +X2,3X+4X4) [5 marks] (b) Determine if the pairs of variables (X1, X3) and (X2, X4) are independent. (5 marks]

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