Show that if (X, Y) bivariate normal( Icirc frac14 x, Icirc frac14 y, Iuml 2X, Iuml 2Y, p), then the following are true (a) The marginal distribution of X is n( Icirc frac14 x, Iuml 2x) and the marginal distribution of Y is n( Icirc frac14 Y, Iuml 2Y) (b) The conditional distribution of Y given X x is (c) For any constants a and b, the distribution of aX bY is n(a1x b sy, a20 b2 2abpxY )

Question: Show that if (X, Y) ~ bivariate normal(Î¼x, Î¼y, Ï2X, Ï2Y, p), then the following are true. (a) The marginal distribution of X is n(Î¼x,

Show that if (X, Y) ~ bivariate normal(Î¼x, Î¼y, Ïƒ2X, Ïƒ2Y, p), then the following are true.
(a) The marginal of X is n(Î¼x, Ïƒ2x) and the marginal of Y is n(Î¼Y, Ïƒ2Y).
(b) The conditional of Y given X = x is

n(a1x + b.sy, a20% + b2+ 2abpxY ).

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