Let (X, Y)^T follow a bivariate normal distribution with E(X) = 3, E(Y) = 4, Var(X) = 25, Var(Y) = 100, and Cov(X, Y) = 50rho, where rho in (-1, 1). If E(Y X = 5) = 4.32, then rho equals

Q23Section ST (Statistics (Q11–Q65))23 of 65

Correlation from conditional mean

Let $(X, Y)^T$ follow a bivariate normal distribution with $E(X) = 3$ , $E(Y) = 4$ , $\operatorname{Var}(X) = 25$ , $\operatorname{Var}(Y) = 100$ , and $\operatorname{Cov}(X, Y) = 50\rho$ , where $\rho \in (-1, 1)$ . If $E(Y | X = 5) = 4.32$ , then $\rho$ equals

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