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Say X and Y are normally distributed random variables, i.e., X,Y ~ N(0,1). For some fixed t and c I know that Pr[X≥t]=c and Pr[Y≥t]=c. Moreover, I also know that X and Y have covariance 0.999.

How can I deduce what Pr[X≥t and Y≥t] roughly is?

Bonus question: what are good references to learn more on related topics for normally distributed random variables?

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up vote 1 down vote accepted

This is the bivariate normal distribution. Here is a paper estimating the cdf of the bivariate normal distribution since no known analytic form is known. This is a good book explaining multivariate normal distributions.

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Thanks for the quick help PEV. –  user915 Jan 26 '11 at 22:15
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