Correlation and Dependence - Bivariate Normal Distribution

Bivariate Normal Distribution

If a pair (X, Y) of random variables follows a bivariate normal distribution, the conditional mean E(X|Y) is a linear function of Y, and the conditional mean E(Y|X) is a linear function of X. The correlation coefficient r between X and Y, along with the marginal means and variances of X and Y, determines this linear relationship:

E(Y|X) = E(Y) + r\sigma_y\frac{X-E(X)}{\sigma_x},

where E(X) and E(Y) are the expected values of X and Y, respectively, and σx and σy are the standard deviations of X and Y, respectively.

Read more about this topic:  Correlation And Dependence

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