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Q65Section ST (Statistics (Q11–Q65))65 of 65

Bivariate normal orthant probability

Let (X,Y)T(X, Y)^T follow a bivariate normal distribution with E(X)=2E(X) = 2, E(Y)=3E(Y) = 3, Var⁡(X)=16\operatorname{Var}(X) = 16, Var⁡(Y)=25\operatorname{Var}(Y) = 25, and Cov⁡(X,Y)=14\operatorname{Cov}(X, Y) = 14. Then 2π(Pr⁡(X>2,Y>3)−14)2\pi (\operatorname{Pr}(X > 2, Y > 3) - \frac{1}{4}) equals __________ (rounded off to two decimal places).

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