Random variables (probability)

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To find the cumulative distribution function (cdf) of random variable Y from the joint cdf of X and Y, taking the limit as x approaches infinity is a straightforward method. Alternatively, one can calculate the joint probability density function (pdf), derive the marginal pdf of Y, and then obtain the cdf from it. However, the limit approach is generally simpler and more efficient for this problem. The discussion emphasizes the ease of using the limit method over the more complex marginalization process. This clarification alleviated concerns about the test question.
TheMathNoob
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Homework Statement


I have the joint cdf of two random variables X and Y and they ask me to find the cdf of just Y. I know that you just take the limit of the cdf as x->infinity, but I am just wondering if you can also do this by calculating the joint pdf and then the marginal of Y and then from the marginal of Y, the cdf of Y.

Homework Equations

The Attempt at a Solution

 
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TheMathNoob said:

Homework Statement


I have the joint cdf of two random variables X and Y and they ask me to find the cdf of just Y. I know that you just take the limit of the cdf as x->infinity, but I am just wondering if you can also do this by calculating the joint pdf and then the marginal of Y and then from the marginal of Y, the cdf of Y.

Homework Equations

The Attempt at a Solution


Yes, sometimes that is how it must be done. However, in your case that would be doing it the hard way, since taking the ##x \to \infty## limit is easier.
 
Ray Vickson said:
Yes, sometimes that is how it must be done. However, in your case that would be doing it the hard way, since taking the ##x \to \infty## limit is easier.
Thank you!, I was so worried about that one in the test.
 

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