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Q52Section C (Section C)52 of 60

Conditional variance in bivariate normal

Let the random vector (X1,X2)(X_1, X_2) follow the bivariate normal distribution with E(X1)=E(X2)=1,Var(X2)=4Var(X1)=4andCov(X1,X2)=1.E(X_1)=E(X_2)=1,\quad \mathrm{Var}(X_2)=4\mathrm{Var}(X_1)=4\quad\text{and}\quad \mathrm{Cov}(X_1, X_2)=1. Then, Var(X1+X2∣X1=12)\mathrm{Var}\left(X_1+X_2 \mid X_1=\frac{1}{2}\right) equals __________

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