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Q33Section ST (Statistics (Q11–Q65))33 of 65

Conditional variance ratio for bivariate normal

Let (X,Y)(X,Y) have a bivariate normal distribution with E(X)=E(Y)=0E(X) = E(Y) = 0. Denote the conditional variance of XX given Y=1Y = 1 by Var⁡(X∣Y=1)\operatorname{Var}(X|Y = 1) and the conditional variance of YY given X=2X = 2 by Var⁡(Y∣X=2)\operatorname{Var}(Y|X = 2). If E(Y∣X=2)E(X∣Y=1)=8\frac{E(Y|X=2)}{E(X|Y=1)} = 8 then Var⁡(Y∣X=2)Var⁡(X∣Y=1)\frac{\operatorname{Var}(Y|X=2)}{\operatorname{Var}(X|Y=1)} equals ________ (in integer).

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