Abstract
Conditional distribution reflects the dependency link among random variables, but two-dimensional random variables Conditional Distribution has some limitations. In order to rich the content of conditional distribution this paper gives the extension of conditional distribution and examples in the case of continuous random variables. For the given definition of conditional distribution of three-dimensional continuous random variables, it also gives the proof. This article obtains the extension strictly in accordance with the definition of two-dimensional random variables and it uses the theory of conditional probability to get the proof. So it can get conditional distributions after changing the condition to enrich the contents of the conditional distribution.
Highlights
The relationships of two-dimensional random variables ( X,Y ) are mainly divided into two types: independence and dependence
This paper is to solve the conditional distribution of multidimensional random variables under the given conditions and its results can be used for teaching, expending the knowledge of the conditional distribution and facilitating people’s calculations
This paper mainly discusses conditional distributions of multidimensional random variables and its related examples given certain conditions in the case of continuous situation. It changes the original condition of one fixed variable into more complex conditions, for example the condition that the sum of two variables is fixed in two-dimensional situation, which is easy to solve with discrete random variables and can be extended in continuous situation
Summary
The relationships of two-dimensional random variables ( X ,Y ) are mainly divided into two types: independence and dependence. Hansen studied nonparametric estimation of smooth conditional distributions; Persi Diaconis, Bernd Sturmfels analyzed conditional distributions using algebraic algorithms for sampling They have shown that the researches of conditional distribution are multi-faceted and more complex while make against undergraduate teaching. In this respect the paper begins to discuss and analyze from the basic content of conditional distribution and educes general formulas with certain conditions on the basis of the definition of conditional distribution. It first starts form the two-dimensional random variable conditional distribution in the case of continuous random variables and changes the given conditions to obtain the extensions of conditional distribution and gives extensions of conditional distribution when there are three-dimensional random variables. This paper is to solve the conditional distribution of multidimensional random variables under the given conditions and its results can be used for teaching, expending the knowledge of the conditional distribution and facilitating people’s calculations
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