“joint probability density function”的概念、定义、翻译、参考文献-科学参考

joint probability density function

Mathematics

For two continuous random variables X and Y, the joint probability density function is the function f such that

$Pr (a \leq X \leq b, c \leq Y \leq d) = \int_{a}^{b} \int_{c}^{d} f (x, y) d y d x .$

Then X and Y are independent if and only if f(x,y) = f_X(x)f_Y(y), where f_X and f_Y are the pdfs of X and Y. The term applies also to the generalization of this to more than two random variables. For two variables, it may be called the bivariate and, for more than two, the multivariate probability density function.

Statistics

单词	joint probability density function
释义	joint probability density function Mathematics For two continuous random variables X and Y, the joint probability density function is the function f such that $Pr (a \leq X \leq b, c \leq Y \leq d) = \int_{a}^{b} \int_{c}^{d} f (x, y) d y d x .$ Then X and Y are independent if and only if f(x,y) = f_X(x)f_Y(y), where f_X and f_Y are the pdfs of X and Y. The term applies also to the generalization of this to more than two random variables. For two variables, it may be called the bivariate and, for more than two, the multivariate probability density function. Statistics See bivariate distribution.
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