“bivariate distribution”的概念、定义、翻译、参考文献-科学参考

bivariate distribution

Statistics

When, as a result of an experiment, values for two random variables X and Y are obtained, it is said that there is a bivariate distribution. In the case of a sample, with n pairs of values (x₁, y₁), (x₂, y₂),…, (x_n, y_n) being obtained, the methods of correlation and regression may be appropriate. Associated with the experiment is a bivariate probability distribution. In the case when X and Y are discrete random variables, the distribution is specified by the joint distribution giving P(X=x_j & Y=y_k) for all values of j and k.
The marginal distribution of X is given by $bivariate distribution$ and the marginal distribution of Y is given by $bivariate distribution$ If X and Y are independent random variables then $bivariate distribution$ The expected values and variances of X and Y are given in the usual way from these marginal distributions. For example, $bivariate distribution$ The conditional distribution of X, given that Y=y_k, is given by $bivariate distribution$ and the conditional expectation of X, given that Y=y_k , written as E(X | Y=y_k), is defined in the usual way as $bivariate distribution$ The conditional distribution of Y and the conditional expectation of Y, given that X=x_j, are defined similarly.
The mutual information of the variables X and Y is given by $bivariate distribution$ The base of the logarithm is usually taken to be 2 (compare diversity index).
In the case when X and Y are continuous random variables, the distribution is specified by the joint probability density function f(x, y) with the property that if R is any region of the (x, y) plane then $bivariate distribution$ The marginal distribution of X then has probability density function (pdf) f_x(x)= and the marginal distribution of Y has pdf f_y(y)=. If the two random variables are independent of one another then f(x, y) is the product of the pdfs of the two marginal distributions. The expected values and variances of X and Y are given in the usual way from these marginal distributions. In this case the mutual information is given by $bivariate distribution$
The probability density function for the conditional distribution of X, given that Y=y, is $bivariate distribution$ and $bivariate distribution$ See also multivariate distribution.

单词	bivariate distribution
释义	bivariate distribution Statistics When, as a result of an experiment, values for two random variables X and Y are obtained, it is said that there is a bivariate distribution. In the case of a sample, with n pairs of values (x₁, y₁), (x₂, y₂),…, (x_n, y_n) being obtained, the methods of correlation and regression may be appropriate. Associated with the experiment is a bivariate probability distribution. In the case when X and Y are discrete random variables, the distribution is specified by the joint distribution giving P(X=x_j & Y=y_k) for all values of j and k. The marginal distribution of X is given by $bivariate distribution$ and the marginal distribution of Y is given by $bivariate distribution$ If X and Y are independent random variables then $bivariate distribution$ The expected values and variances of X and Y are given in the usual way from these marginal distributions. For example, $bivariate distribution$ The conditional distribution of X, given that Y=y_k, is given by $bivariate distribution$ and the conditional expectation of X, given that Y=y_k , written as E(X \| Y=y_k), is defined in the usual way as $bivariate distribution$ The conditional distribution of Y and the conditional expectation of Y, given that X=x_j, are defined similarly. The mutual information of the variables X and Y is given by $bivariate distribution$ The base of the logarithm is usually taken to be 2 (compare diversity index). In the case when X and Y are continuous random variables, the distribution is specified by the joint probability density function f(x, y) with the property that if R is any region of the (x, y) plane then $bivariate distribution$ The marginal distribution of X then has probability density function (pdf) f_x(x)= and the marginal distribution of Y has pdf f_y(y)=. If the two random variables are independent of one another then f(x, y) is the product of the pdfs of the two marginal distributions. The expected values and variances of X and Y are given in the usual way from these marginal distributions. In this case the mutual information is given by $bivariate distribution$ The probability density function for the conditional distribution of X, given that Y=y, is $bivariate distribution$ and $bivariate distribution$ See also multivariate distribution.
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