Question: Let ( X UX 2) follow a bivariate normal distribution with E ( X 0 = E ( X 2) = 0, V(X x) =

Let ( X UX 2) follow a bivariate normal distribution with E ( X 0 = E ( X 2) = 0, V(X x) = V(X2) = 1.

Let the coefficient of correlation between X x and X 2 be equal to p.

Find the distribution of Y2 — Y u where Y2 = max(XuX 2), Y x = m i n ^ , ^ ) .

Calculate the probability P{Y2 > 0}. Show that

E(Y) = -(1-9)". E(Y) = = (1 = 9)". 1/2

E(Y) = -(1-9)". E(Y) = = (1 = 9)". 1/2

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