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This is a case of bivariate normal as there are two normal variables (as opposed to two variables driven by the same common random factor). The answer to your question is the conditional distribution of one of the variables given the other variable: $Y|X \sim N\left(\mu_y+\rho \sigma_y \frac{x-\mu_x}{\sigma_x}, \sigma_y^2 \left(1-\rho^2\right) \right)$ For ...


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