Suppose we have a bivariate normal (X, Y), whose mean is zero, and variance 1, and correlation \rho. Is there an easy formula for P(X < x | Y < y ) ?


marked as duplicate by whuber Dec 30 '17 at 22:28

This question was marked as an exact duplicate of an existing question.

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    $\begingroup$ You use the definition of conditional probability and will notice that it is just the joint cdf over the marginal cdf. $\endgroup$ – Megadeth Dec 30 '17 at 21:25


$$ \int_{-\infty}^x \frac{\int_{-\infty}^{y} f_{X,Y}(u,v) dv}{ \int_{-\infty}^{y}f_{Y}(v) dv} du $$

Didn't even require normality.


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