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:
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:
“You know that fiction, prose rather, is possibly the roughest trade of all in writing. You do not have the reference, the old important reference. You have the sheet of blank paper, the pencil, and the obligation to invent truer than things can be true. You have to take what is not palpable and make it completely palpable and also have it seem normal and so that it can become a part of experience of the person who reads it.”
—Ernest Hemingway (18991961)
“The man who pretends that the distribution of income in this country reflects the distribution of ability or character is an ignoramus. The man who says that it could by any possible political device be made to do so is an unpractical visionary. But the man who says that it ought to do so is something worse than an ignoramous and more disastrous than a visionary: he is, in the profoundest Scriptural sense of the word, a fool.”
—George Bernard Shaw (18561950)