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:

    “Our normal waking consciousness, rational consciousness as we call it, is but one special type of consciousness, whilst all about it, parted from it by the filmiest of screens, there lie potential forms of consciousness entirely different.”
    —William James (1842–1910)

    “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)