Exploring the Marginal CDF of X with Two Random Variables

In summary, the conversation discusses the marginal CDF of a random variable X and the conditions under which it can be obtained. The speaker also presents an expression for the marginal CDF and questions its correctness and applicability.
  • #1
zli034
107
0
If there are X and Y two random variables. The pdf of Y is f(y), and conditional pdf of X is f(x|y). I want to find the marginal CDF of X, the F(x). Is this correct?
[itex]F(x)=\int^{F(x|y)}_{-\infty}f(y)dy[/itex]

[itex] \dfrac{d}{dx}\int^{F(x|y)}_{-\infty}f(y)dy=\int^{\infty}_{-\infty}f(x|y)f(y)dy=f(x)[/itex]?
 
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  • #2
The density function for x is [itex]\int_{-\infty}^{\infty}f(x|y)f(y)dy[/itex].
 
  • #3
Yes, I know your logic. But I found the marginal expression today. I put it here. I want to know is it correct, or under what condition I can get F(x) that way?
 
  • #4
zli034 said:
Yes, I know your logic. But I found the marginal expression today. I put it here. I want to know is it correct, or under what condition I can get F(x) that way?
It is not obvious. [itex]F(x)=\int_{-\infty}^{\infty}F(x|y)f(y)dy[/itex]. I don't see how you got your integral.
 
  • #5
zli034 said:
Is this correct?

No. And I don't see any distribution for which it is correct.
 

1. What is a marginal CDF?

A marginal CDF, or cumulative distribution function, is a mathematical function that gives the probability that a random variable X is less than or equal to a certain value x. It is a useful tool in probability and statistics for understanding the distribution of a particular variable.

2. How do you find the marginal CDF of X?

To find the marginal CDF of X, you need to first determine the probability density function (PDF) of X. Then, you can integrate the PDF from negative infinity to x to get the CDF. The resulting function will give you the probability that X is less than or equal to x.

3. What does the marginal CDF tell us?

The marginal CDF tells us the probability that a random variable X is less than or equal to a certain value x. This can be useful for understanding the likelihood of certain events occurring and for making predictions based on the distribution of X.

4. How is the marginal CDF related to the marginal PDF?

The marginal CDF and marginal PDF are closely related. The marginal PDF is the derivative of the marginal CDF, and the marginal CDF is the integral of the marginal PDF. In other words, the marginal CDF is the cumulative version of the marginal PDF.

5. Can the marginal CDF be used for any type of random variable?

Yes, the marginal CDF can be used for any type of random variable, including discrete and continuous variables. However, the method for finding the marginal CDF may differ depending on the type of variable and its PDF.

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