Question: Let (x, y) be bivariate normal with zero means, unit variances and correlation ????, and let ???? be a monotone ???? -function. Show that E(????(x)????(y))

Let (x, y) be bivariate normal with zero means, unit variances and correlation ????, and let ???? be a monotone ???? -function. Show that E(????(x)????(y)) is an increasing function of ???? (Hint: y = ????x +

√1 − ????2z with z ∼ (0, 1) independent of x).

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