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

Famous quotes containing the words normal and/or distribution:

    “As blacks, we need not be afraid that encouraging moral development, a conscience and guilt will prevent social action. Black children without the ability to feel a normal amount of guilt will victimize their parents, relatives and community first. They are unlikely to be involved in social action to improve the black community. Their self-centered personalities will cause them to look out for themselves without concern for others, black or white.”
    —James P. Comer (20th century)

    “Classical and romantic: private language of a family quarrel, a dead dispute over the distribution of emphasis between man and nature.”
    —Cyril Connolly (1903–1974)