joint distribution function
Practical problems. The results of some random experiments need to be described by two or more random variables at the same time. For example, to
observe the physical condition of students according to their height X and weight Y, this is not only the situation of X and Y, but also the relationship between them.
Joint distribution function of two-dimensional random variables
Two-dimensional continuous random variable
If all possible values of the two-dimensional random variable (X, Y) cannot be listed one by one, but take any point in a certain interval of the plane, then we call it a two-dimensional continuous random variable, which is similar to the one-dimensional accessory variable. The distribution function F(x,y) and the probability density function f(x,y) of the two-dimensional random variables X and Y have the following relationship
marginal distribution
The distribution function F(x, y) of a two-dimensional random variable (X, Y) is an overall description of the probability characteristics of the random variable (X, y), and they are all one-dimensional random variables, and they also have their own one-dimensional distribution functions. What is the relationship between these distribution functions?
The marginal distribution is defined as follows:
where the marginal distribution functions Fx(x), FY(y) can be determined by the distribution function F(xy), that is, when one of the variables Y takes all possible values, the probability distribution of the corresponding interval of the other variable X
