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Conditional distribution of a bivariate normal variable

Conditionally on

X_{2} = x_{2}

,

X_{1} \sim N (μ_{1} + ρ \frac{σ _{1}}{σ _{2}} (x_{2} - μ_{2}), σ_{1}^{2} (1 - ρ^{2})) .

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